module RGL::Graph
In BGL terminology the module Graph
defines the graph concept (see www.boost.org/libs/graph/doc/graph_concepts.html). We however do not distinguish between the IncidenceGraph, EdgeListGraph and VertexListGraph concepts, which would complicate the interface too much. These concepts are defined in BGL to differentiate between efficient access to edges and vertices.
The RGL
Graph
concept contains only a few requirements that are common to all the graph concepts. These include, especially, the iterators defining the sets of vertices and edges (see each_vertex
and each_adjacent
). Most other functions are derived from these fundamental iterators, i.e. num_vertices
or num_edges.
Each graph is an enumerable of vertices.
Public Instance Methods
Returns true if the graph contains no cycles. This is only meaningful for directed graphs. Returns false for undirected graphs.
# File lib/rgl/topsort.rb 73 def acyclic? 74 topsort_iterator.length == num_vertices 75 end
Returns an array of vertices adjacent to vertex v.
# File lib/rgl/base.rb 215 def adjacent_vertices(v) 216 r = [] 217 each_adjacent(v) { |u| r << u } 218 r 219 end
Finds the shortest paths from the source to each vertex of the graph.
Returns a Hash that maps each vertex of the graph to an Array of vertices that represents the shortest path from the source to the vertex. If the path doesn't exist, the corresponding hash value is nil. For the source vertex returned hash contains a trivial one-vertex path - [source].
Unlike Dijkstra algorithm, Bellman-Ford shortest paths algorithm works with negative edge weights.
Raises ArgumentError if an edge weight is undefined.
Raises ArgumentError or the graph has negative-weight cycles. This behavior can be overridden my a custom handler for visitor's edge_not_minimized event.
# File lib/rgl/bellman_ford.rb 108 def bellman_ford_shortest_paths(edge_weights_map, source, visitor = BellmanFordVisitor.new(self)) 109 BellmanFordAlgorithm.new(self, edge_weights_map, visitor).shortest_paths(source) 110 end
Returns a BFSIterator
, starting at vertex v.
# File lib/rgl/traversal.rb 106 def bfs_iterator(v = self.detect { |x| true }) 107 BFSIterator.new(self, v) 108 end
Returns a DirectedAdjacencyGraph
, which represents a BFS search tree starting at v. This method uses the tree_edge_event of BFSIterator
to record all tree edges of the search tree in the result.
# File lib/rgl/traversal.rb 114 def bfs_search_tree_from(v) 115 require 'rgl/adjacency' 116 bfs = bfs_iterator(v) 117 tree = DirectedAdjacencyGraph.new 118 119 bfs.set_tree_edge_event_handler do |from, to| 120 tree.add_edge(from, to) 121 end 122 123 bfs.set_to_end # does the search 124 tree 125 end
Returns true if the graph is bipartite. Otherwise returns false.
# File lib/rgl/bipartite.rb 38 def bipartite? 39 !bipartite_sets.nil? 40 end
Separates graph's vertices into two disjoint sets so that every edge of the graph connects vertices from different sets. If it's possible, the graph is bipartite.
Returns an array of two disjoint vertices sets (represented as arrays) if the graph is bipartite. Otherwise, returns nil.
# File lib/rgl/bipartite.rb 14 def bipartite_sets 15 raise NotUndirectedError.new('bipartite sets can only be found for an undirected graph') if directed? 16 17 bfs = BipartiteBFSIterator.new(self) 18 19 # if necessary, we start BFS from each vertex to make sure 20 # that all connected components of the graph are processed 21 each_vertex do |u| 22 next if bfs.finished_vertex?(u) 23 24 bfs.reset_start(u) 25 bfs.move_forward_until { bfs.found_odd_cycle } 26 27 return if bfs.found_odd_cycle 28 end 29 30 bfs.bipartite_sets_map.inject([[], []]) do |sets, (vertex, set)| 31 sets[set] << vertex 32 sets 33 end 34 end
Returns an RGL::ImplicitGraph
where the strongly connected components of this graph are condensed into single nodes represented by Set instances containing the members of each strongly connected component. Edges between the different strongly connected components are preserved while edges within strongly connected components are omitted.
Raises RGL::NotDirectedError
if run on an undirected graph.
# File lib/rgl/condensation.rb 17 def condensation_graph 18 raise NotDirectedError, 19 "condensation_graph only supported for directed graphs" unless directed? 20 21 # Get the component map for the strongly connected components. 22 comp_map = strongly_connected_components.comp_map 23 24 # Invert the map such that for any number, n, in the component map a Set 25 # instance is created containing all of the nodes which map to n. The Set 26 # instances will be used to map to the number, n, with which the elements 27 # of the set are associated. 28 inv_comp_map = {} 29 comp_map.each { |v, n| (inv_comp_map[n] ||= Set.new) << v } 30 31 # Create an ImplicitGraph where the nodes are the strongly connected 32 # components of this graph and the edges are the edges of this graph which 33 # cross between the strongly connected components. 34 ImplicitGraph.new do |g| 35 g.vertex_iterator do |b| 36 inv_comp_map.each_value(&b) 37 end 38 39 g.adjacent_iterator do |scc, b| 40 scc.each do |v| 41 each_adjacent(v) do |w| 42 # Do not make the cluster reference itself in the graph. 43 if comp_map[v] != comp_map[w] 44 b.call(inv_comp_map[comp_map[w]]) 45 end 46 end 47 end 48 end 49 50 g.directed = true 51 end 52 end
Do a recursive DFS search on the whole graph. If a block is passed, it is called on each finish_vertex event. See strongly_connected_components
for an example usage.
Note that this traversal does not garantee, that roots are at the top of each spanning subtree induced by the DFS search on a directed graph (see also the discussion in issue #20).
# File lib/rgl/traversal.rb 179 def depth_first_search(vis = DFSVisitor.new(self), &b) 180 each_vertex do |u| 181 unless vis.finished_vertex?(u) 182 vis.handle_start_vertex(u) 183 depth_first_visit(u, vis, &b) 184 end 185 end 186 end
Start a depth first search at vertex u. The block b is called on each finish_vertex event.
# File lib/rgl/traversal.rb 191 def depth_first_visit(u, vis = DFSVisitor.new(self), &b) 192 vis.color_map[u] = :GRAY 193 vis.handle_examine_vertex(u) 194 195 each_adjacent(u) do |v| 196 vis.handle_examine_edge(u, v) 197 198 if vis.follow_edge?(u, v) # (u,v) is a tree edge 199 vis.handle_tree_edge(u, v) # also discovers v 200 vis.color_map[v] = :GRAY # color of v was :WHITE 201 depth_first_visit(v, vis, &b) 202 else # (u,v) is a non tree edge 203 if vis.color_map[v] == :GRAY 204 vis.handle_back_edge(u, v) # (u,v) has gray target 205 else 206 vis.handle_forward_edge(u, v) # (u,v) is a cross or forward edge 207 end 208 end 209 end 210 211 vis.color_map[u] = :BLACK 212 vis.handle_finish_vertex(u) # finish vertex 213 b.call(u) 214 end
Returns a DFSIterator
staring at vertex v.
# File lib/rgl/traversal.rb 167 def dfs_iterator(v = self.detect { |x| true }) 168 DFSIterator.new(self, v) 169 end
Finds the shortest path from the source to the target in the graph.
If the path exists, returns it as an Array of vertices. Otherwise, returns nil.
Raises ArgumentError if edge weight is negative or undefined.
# File lib/rgl/dijkstra.rb 114 def dijkstra_shortest_path(edge_weights_map, source, target, visitor = DijkstraVisitor.new(self)) 115 DijkstraAlgorithm.new(self, edge_weights_map, visitor).shortest_path(source, target) 116 end
Finds the shortest paths from the source to each vertex of the graph.
Returns a Hash that maps each vertex of the graph to an Array of vertices that represents the shortest path from the source to the vertex. If the path doesn't exist, the corresponding hash value is nil. For the source vertex returned hash contains a trivial one-vertex path - [source].
Raises ArgumentError if edge weight is negative or undefined.
# File lib/rgl/dijkstra.rb 126 def dijkstra_shortest_paths(edge_weights_map, source, visitor = DijkstraVisitor.new(self)) 127 DijkstraAlgorithm.new(self, edge_weights_map, visitor).shortest_paths(source) 128 end
Is the graph directed? The default returns false.
# File lib/rgl/base.rb 174 def directed? 175 false 176 end
Call dotty for the graph which is written to the file 'graph.dot' in the current directory.
# File lib/rgl/dot.rb 73 def dotty(params = {}) 74 dotfile = "graph.dot" 75 File.open(dotfile, "w") do |f| 76 print_dotted_on(params, f) 77 end 78 unless system("dotty", dotfile) 79 raise "Error executing dotty. Did you install GraphViz?" 80 end 81 end
Vertices get enumerated. A graph is thus an enumerable of vertices.
# File lib/rgl/base.rb 168 def each(&block) 169 each_vertex(&block) 170 end
The each_adjacent
iterator defines the out edges of vertex v. This method must be defined by concrete graph classes. Its defines the BGL IncidenceGraph concept.
# File lib/rgl/base.rb 144 def each_adjacent(v) # :yields: v 145 raise NotImplementedError 146 end
Compute the connected components of an undirected graph, using a DFS (Depth-first search)-based approach. A _connected component_ of an undirected graph is a set of vertices that are all reachable from each other.
The function is implemented as an iterator which calls the client with an array of vertices for each component.
It raises an exception if the graph is directed.
# File lib/rgl/connected_components.rb 23 def each_connected_component 24 raise NotUndirectedError, 25 "each_connected_component only works " + 26 "for undirected graphs." if directed? 27 28 comp = [] 29 vis = DFSVisitor.new(self) 30 vis.set_finish_vertex_event_handler { |v| comp << v } 31 32 vis.set_start_vertex_event_handler do |v| 33 yield comp unless comp.empty? 34 comp = [] 35 end 36 37 depth_first_search(vis) { |v| } 38 yield comp unless comp.empty? 39 end
The each_edge
iterator should provide efficient access to all edges of the graph. Its defines the EdgeListGraph concept.
This method must not be defined by concrete graph classes, because it can be implemented using each_vertex
and each_adjacent. However for undirected graph the function is inefficient because we must not yield (v,u) if we already visited edge (u,v).
# File lib/rgl/base.rb 156 def each_edge(&block) 157 if directed? 158 each_vertex do |u| 159 each_adjacent(u) { |v| yield u, v } 160 end 161 else 162 each_edge_aux(&block) # concrete graphs should to this better 163 end 164 end
The each_vertex
iterator defines the set of vertices. This method must be defined by concrete graph classes. It defines the BGL VertexListGraph concept.
# File lib/rgl/base.rb 136 def each_vertex() # :yields: v 137 raise NotImplementedError 138 end
Returns the class for edges: DirectedEdge or UnDirectedEdge.
# File lib/rgl/base.rb 200 def edge_class 201 directed? ? DirectedEdge : UnDirectedEdge 202 end
Return the array of edges (DirectedEdge or UnDirectedEdge) of the graph using each_edge
, depending whether the graph is directed or not.
# File lib/rgl/base.rb 206 def edges 207 result = [] 208 c = edge_class 209 each_edge { |u, v| result << c.new(u, v) } 210 result 211 end
Return a new ImplicitGraph
which has as edges all edges of the receiver which satisfy the predicate filter (a block with two parameters).
Example¶ ↑
g = complete(7).edges_filtered_by { |u,v| u+v == 7 } g.to_s => "(1=6)(2=5)(3=4)" g.vertices => [1, 2, 3, 4, 5, 6, 7]
# File lib/rgl/implicit.rb 145 def edges_filtered_by(&filter) 146 implicit_graph do |g| 147 g.adjacent_iterator do |v, b| 148 self.each_adjacent(v) do |u| 149 b.call(u) if filter.call(v, u) 150 end 151 end 152 153 g.edge_iterator do |b| 154 self.each_edge { |u, v| b.call(u, v) if filter.call(u, v) } 155 end 156 end 157 end
Returns true if the graph has no vertices, i.e. num_vertices
== 0.
# File lib/rgl/base.rb 188 def empty? 189 num_vertices.zero? 190 end
Two graphs are equal iff they have equal directed? property as well as vertices and edges sets.
# File lib/rgl/base.rb 254 def eql?(other) 255 equal?(other) || eql_graph?(other) 256 end
Returns true if v is a vertex of the graph. Same as include? inherited from Enumerable. Complexity is O(num_vertices
) by default. Concrete graph may be better here (see AdjacencyGraph
).
# File lib/rgl/base.rb 182 def has_vertex?(v) 183 include?(v) # inherited from enumerable 184 end
Return a new ImplicitGraph
which is isomorphic (i.e. has same edges and vertices) to the receiver. It is a shortcut, also used by edges_filtered_by
and vertices_filtered_by.
# File lib/rgl/implicit.rb 163 def implicit_graph 164 result = ImplicitGraph.new do |g| 165 g.vertex_iterator { |b| self.each_vertex(&b) } 166 g.adjacent_iterator { |v, b| self.each_adjacent(v, &b) } 167 g.directed = self.directed? 168 end 169 170 yield result if block_given? # let client overwrite defaults 171 result 172 end
Finds the maximum flow from the source to the sink in the graph.
Returns flows map as a hash that maps each edge of the graph to a flow through that edge that is required to reach the maximum total flow.
For the method to work, the graph should be first altered so that for each directed edge (u, v) it contains reverse edge (u, v). Capacities of the primary edges should be non-negative, while reverse edges should have zero capacity.
Raises ArgumentError if the graph is not directed.
Raises ArgumentError if a reverse edge is missing, edge capacity is missing, an edge has negative capacity, or a reverse edge has positive capacity.
# File lib/rgl/edmonds_karp.rb 130 def maximum_flow(edge_capacities_map, source, sink) 131 EdmondsKarpAlgorithm.new(self, edge_capacities_map).maximum_flow(source, sink) 132 end
Returns the number of edges.
# File lib/rgl/base.rb 240 def num_edges 241 r = 0 242 each_edge { |u, v| r +=1 } 243 r 244 end
Returns the number of out-edges (for directed graphs) or the number of incident edges (for undirected graphs) of vertex v.
# File lib/rgl/base.rb 224 def out_degree(v) 225 r = 0 226 each_adjacent(v) { |u| r += 1 } 227 r 228 end
Checks whether a path exists between source and target vertices in the graph.
# File lib/rgl/path.rb 10 def path?(source, target) 11 return false unless has_vertex?(source) 12 13 bfs_iterator = bfs_iterator(source) 14 bfs_iterator.include?(target) 15 end
Finds the minimum spanning tree of the graph.
Returns an AdjacencyGraph
that represents the minimum spanning tree of the graph's connectivity component that contains the starting vertex. The algorithm starts from an arbitrary vertex if the start_vertex is not given. Since the implementation relies on the Dijkstra's algorithm, Prim's algorithm uses the same visitor class and emits the same events.
Raises ArgumentError if edge weight is undefined.
# File lib/rgl/prim.rb 46 def prim_minimum_spanning_tree(edge_weights_map, start_vertex = nil, visitor = DijkstraVisitor.new(self)) 47 PrimAlgorithm.new(self, edge_weights_map, visitor).minimum_spanning_tree(start_vertex) 48 end
Output the DOT-graph to stream s.
# File lib/rgl/dot.rb 66 def print_dotted_on(params = {}, s = $stdout) 67 s << to_dot_graph(params).to_s << "\n" 68 end
Return a new DirectedAdjacencyGraph
which has the same set of vertices. If (u,v) is an edge of the graph, then (v,u) is an edge of the result.
If the graph is undirected, the result is self.
# File lib/rgl/adjacency.rb 189 def reverse 190 return self unless directed? 191 result = DirectedAdjacencyGraph.new 192 each_vertex { |v| result.add_vertex v } 193 each_edge { |u, v| result.add_edge(v, u) } 194 result 195 end
Returns the number of vertices.
# File lib/rgl/base.rb 232 def size # Why not in Enumerable? 233 inject(0) { |n, v| n + 1 } 234 end
This is Tarjan's algorithm for strongly connected components, from his paper “Depth first search and linear graph algorithms”. It calculates the components in a single application of DFS. We implement the algorithm with the help of the DFSVisitor
TarjanSccVisitor
.
Definition¶ ↑
A _strongly connected component_ of a directed graph G=(V,E) is a maximal set of vertices U which is in V, such that for every pair of vertices u and v in U, we have both a path from u to v and a path from v to u. That is to say, u and v are reachable from each other.
@Article!{Tarjan:1972:DFS,
author = "R. E. Tarjan", key = "Tarjan", title = "Depth First Search and Linear Graph Algorithms", journal = "SIAM Journal on Computing", volume = "1", number = "2", pages = "146--160", month = jun, year = "1972", CODEN = "SMJCAT", ISSN = "0097-5397 (print), 1095-7111 (electronic)", bibdate = "Thu Jan 23 09:56:44 1997", bibsource = "Parallel/Multi.bib, Misc/Reverse.eng.bib",
}
The output of the algorithm is recorded in a TarjanSccVisitor
vis. vis.comp_map will contain numbers giving the component ID assigned to each vertex. The number of components is vis.num_comp.
# File lib/rgl/connected_components.rb 135 def strongly_connected_components 136 raise NotDirectedError, 137 "strong_components only works for directed graphs." unless directed? 138 139 vis = TarjanSccVisitor.new(self) 140 depth_first_search(vis) { |v| } 141 vis 142 end
Convert a general graph to an AdjacencyGraph
. If the graph is directed, returns a DirectedAdjacencyGraph
; otherwise, returns an AdjacencyGraph
.
# File lib/rgl/adjacency.rb 177 def to_adjacency 178 result = (directed? ? DirectedAdjacencyGraph : AdjacencyGraph).new 179 each_vertex { |v| result.add_vertex(v) } 180 each_edge { |u, v| result.add_edge(u, v) } 181 result 182 end
Return a RGL::DOT::Digraph
for directed graphs or a DOT::Graph
for an undirected Graph
. params can contain any graph property specified in rdot.rb.
# File lib/rgl/dot.rb 31 def to_dot_graph(params = {}) 32 params['name'] ||= self.class.name.gsub(/:/, '_') 33 fontsize = params['fontsize'] ? params['fontsize'] : '8' 34 graph = (directed? ? DOT::Digraph : DOT::Graph).new(params) 35 edge_class = directed? ? DOT::DirectedEdge : DOT::Edge 36 vertex_options = params['vertex'] || {} 37 edge_options = params['edge'] || {} 38 39 each_vertex do |v| 40 default_vertex_options = { 41 'name' => vertex_id(v), 42 'fontsize' => fontsize, 43 'label' => vertex_label(v) 44 } 45 each_vertex_options = default_vertex_options.merge(vertex_options) 46 vertex_options.each{|option, val| each_vertex_options[option] = val.call(v) if val.is_a?(Proc)} 47 graph << DOT::Node.new(each_vertex_options) 48 end 49 50 each_edge do |u, v| 51 default_edge_options = { 52 'from' => vertex_id(u), 53 'to' => vertex_id(v), 54 'fontsize' => fontsize 55 } 56 each_edge_options = default_edge_options.merge(edge_options) 57 edge_options.each{|option, val| each_edge_options[option] = val.call(u, v) if val.is_a?(Proc)} 58 graph << edge_class.new(each_edge_options) 59 end 60 61 graph 62 end
Utility method to show a string representation of the edges of the graph.
# File lib/rgl/base.rb 248 def to_s 249 edges.collect {|e| e.to_s}.sort.join 250 end
Return a new AdjacencyGraph
which has the same set of vertices. If (u,v) is an edge of the graph, then (u,v) and (v,u) (which are the same edges) are edges of the result.
If the graph is undirected, the result is self.
# File lib/rgl/adjacency.rb 203 def to_undirected 204 return self unless directed? 205 AdjacencyGraph.new(Set, self) 206 end
Returns a TopsortIterator
.
# File lib/rgl/topsort.rb 66 def topsort_iterator 67 TopsortIterator.new(self) 68 end
Returns an RGL::DirectedAdjacencyGraph
which is the transitive closure of this graph. Meaning, for each path u -> … -> v in this graph, the path is copied and the edge u -> v is added. This method supports working with cyclic graphs by ensuring that edges are created between every pair of vertices in the cycle, including self-referencing edges.
This method should run in O(|V||E|) time, where |V| and |E| are the number of vertices and edges respectively.
Raises RGL::NotDirectedError
if run on an undirected graph.
# File lib/rgl/transitivity.rb 20 def transitive_closure 21 raise NotDirectedError, 22 "transitive_closure only supported for directed graphs" unless directed? 23 24 # Compute a condensation graph in order to hide cycles. 25 cg = condensation_graph 26 27 # Use a depth first search to calculate the transitive closure over the 28 # condensation graph. This ensures that as we traverse up the graph we 29 # know the transitive closure of each subgraph rooted at each node 30 # starting at the leaves. Subsequent root nodes which consume these 31 # subgraphs by way of the nodes' immediate successors can then immediately 32 # add edges to the roots of the subgraphs and to every successor of those 33 # roots. 34 tc_cg = DirectedAdjacencyGraph.new 35 cg.depth_first_search do |v| 36 # For each vertex v, w, and x where the edges v -> w and w -> x exist in 37 # the source graph, add edges v -> w and v -> x to the target graph. 38 cg.each_adjacent(v) do |w| 39 tc_cg.add_edge(v, w) 40 tc_cg.each_adjacent(w) do |x| 41 tc_cg.add_edge(v, x) 42 end 43 end 44 # Ensure that a vertex with no in or out edges is added to the graph. 45 tc_cg.add_vertex(v) 46 end 47 48 # Expand the condensed transitive closure. 49 # 50 # For each trivial strongly connected component in the condensed graph, 51 # add the single node it contains to the new graph and add edges for each 52 # edge the node begins in the original graph. 53 # For each NON-trivial strongly connected component in the condensed 54 # graph, add each node it contains to the new graph and add edges to 55 # every node in the strongly connected component, including self 56 # referential edges. Then for each edge of the original graph from any 57 # of the contained nodes, add edges from each of the contained nodes to 58 # all the edge targets. 59 g = DirectedAdjacencyGraph.new 60 tc_cg.each_vertex do |scc| 61 scc.each do |v| 62 # Add edges between all members of non-trivial strongly connected 63 # components (size > 1) and ensure that self referential edges are 64 # added when necessary for trivial strongly connected components. 65 if scc.size > 1 || has_edge?(v, v) 66 scc.each do |w| 67 g.add_edge(v, w) 68 end 69 end 70 # Ensure that a vertex with no in or out edges is added to the graph. 71 g.add_vertex(v) 72 end 73 # Add an edge from every member of a strongly connected component to 74 # every member of each strongly connected component to which the former 75 # points. 76 tc_cg.each_adjacent(scc) do |scc2| 77 scc.each do |v| 78 scc2.each do |w| 79 g.add_edge(v, w) 80 end 81 end 82 end 83 end 84 85 # Finally, the transitive closure... 86 g 87 end
Returns an RGL::DirectedAdjacencyGraph
which is the transitive reduction of this graph. Meaning, that each edge u -> v is omitted if path u -> … -> v exists. This method supports working with cyclic graphs; however, cycles are arbitrarily simplified which may lead to variant, although equally valid, results on equivalent graphs.
This method should run in O(|V||E|) time, where |V| and |E| are the number of vertices and edges respectively.
Raises RGL::NotDirectedError
if run on an undirected graph.
# File lib/rgl/transitivity.rb 100 def transitive_reduction 101 raise NotDirectedError, 102 "transitive_reduction only supported for directed graphs" unless directed? 103 104 # Compute a condensation graph in order to hide cycles. 105 cg = condensation_graph 106 107 # Use a depth first search to compute the transitive reduction over the 108 # condensed graph. This is similar to the computation of the transitive 109 # closure over the graph in that for any node of the graph all nodes 110 # reachable from the node are tracked. Using a depth first search ensures 111 # that all nodes reachable from a target node are known when considering 112 # whether or not to add an edge pointing to that target. 113 tr_cg = DirectedAdjacencyGraph.new 114 paths_from = {} 115 cg.depth_first_search do |v| 116 paths_from[v] = Set.new 117 cg.each_adjacent(v) do |w| 118 # Only add the edge v -> w if there is no other edge v -> x such that 119 # w is reachable from x. Make sure to completely skip the case where 120 # x == w. 121 unless cg.to_enum(:each_adjacent, v).any? { |x| x != w && paths_from[x].include?(w) } 122 tr_cg.add_edge(v, w) 123 124 # For each vertex v, track all nodes reachable from v by adding node 125 # w to the list as well as all the nodes readable from w. 126 paths_from[v] << w 127 paths_from[v].merge(paths_from[w]) 128 end 129 end 130 # Ensure that a vertex with no in or out edges is added to the graph. 131 tr_cg.add_vertex(v) 132 end 133 134 # Expand the condensed transitive reduction. 135 # 136 # For each trivial strongly connected component in the condensed graph, 137 # add the single node it contains to the new graph and add edges for each 138 # edge the node begins in the original graph. 139 # For each NON-trivial strongly connected component in the condensed 140 # graph, add each node it contains to the new graph and add arbitrary 141 # edges between the nodes to form a simple cycle. Then for each strongly 142 # connected component adjacent to the current one, find and add the first 143 # edge which exists in the original graph, starts in the first strongly 144 # connected component, and ends in the second strongly connected 145 # component. 146 g = DirectedAdjacencyGraph.new 147 tr_cg.each_vertex do |scc| 148 # Make a cycle of the contents of non-trivial strongly connected 149 # components. 150 scc_arr = scc.to_a 151 if scc.size > 1 || has_edge?(scc_arr.first, scc_arr.first) 152 0.upto(scc_arr.size - 2) do |idx| 153 g.add_edge(scc_arr[idx], scc_arr[idx + 1]) 154 end 155 g.add_edge(scc_arr.last, scc_arr.first) 156 end 157 158 # Choose a single edge between the members of two different strongly 159 # connected component to add to the graph. 160 edges = self.to_enum(:each_edge) 161 tr_cg.each_adjacent(scc) do |scc2| 162 g.add_edge( 163 *edges.find do |v, w| 164 scc.member?(v) && scc2.member?(w) 165 end 166 ) 167 end 168 169 # Ensure that a vertex with no in or out edges is added to the graph. 170 scc.each do |v| 171 g.add_vertex(v) 172 end 173 end 174 175 # Finally, the transitive reduction... 176 g 177 end
# File lib/rgl/dot.rb 23 def vertex_id(v) 24 v 25 end
Returns a label for vertex v. Default is v.to_s
# File lib/rgl/dot.rb 19 def vertex_label(v) 20 v.to_s 21 end
Return the array of vertices. Synonym for to_a inherited by Enumerable.
# File lib/rgl/base.rb 194 def vertices 195 to_a 196 end
Graph
adaptors¶ ↑
Return a new ImplicitGraph
which has as vertices all vertices of the receiver which satisfy the predicate filter.
The methods provides similar functionality as the BGL graph adapter filtered_graph (see BOOST_DOC/filtered_graph.html).
Example¶ ↑
def complete (n) set = n.integer? ? (1..n) : n RGL::ImplicitGraph.new do |g| g.vertex_iterator { |b| set.each(&b) } g.adjacent_iterator do |x, b| set.each { |y| b.call(y) unless x == y } end end end complete(4).to_s # => "(1=2)(1=3)(1=4)(2=3)(2=4)(3=4)" complete(4).vertices_filtered_by { |v| v != 4 }.to_s # => "(1=2)(1=3)(2=3)"
# File lib/rgl/implicit.rb 124 def vertices_filtered_by(&filter) 125 implicit_graph do |g| 126 g.vertex_iterator do |b| 127 self.each_vertex { |v| b.call(v) if filter.call(v) } 128 end 129 130 g.adjacent_iterator do |v, b| 131 self.each_adjacent(v) { |u| b.call(u) if filter.call(u) } 132 end 133 end 134 end
Use dot to create a graphical representation of the graph. Returns the filename of the graphics file.
# File lib/rgl/dot.rb 86 def write_to_graphic_file(fmt='png', dotfile="graph", options={}) 87 src = dotfile + ".dot" 88 dot = dotfile + "." + fmt 89 90 File.open(src, 'w') do |f| 91 f << self.to_dot_graph(options).to_s << "\n" 92 end 93 94 unless system("dot -T#{fmt} #{src} -o #{dot}") 95 raise "Error executing dot. Did you install GraphViz?" 96 end 97 dot 98 end
Private Instance Methods
# File lib/rgl/base.rb 294 def each_edge_aux 295 # needed in each_edge 296 visited = Hash.new 297 298 each_vertex do |u| 299 each_adjacent(u) do |v| 300 edge = UnDirectedEdge.new(u, v) 301 302 unless visited.has_key?(edge) 303 visited[edge] = true 304 yield u, v 305 end 306 end 307 end 308 end
# File lib/rgl/base.rb 280 def eql_edges_set?(other) 281 other_num_edges = 0 282 283 other.each_edge do |u, v| 284 if has_edge?(u, v) 285 other_num_edges += 1 286 else 287 return false 288 end 289 end 290 291 other_num_edges == num_edges 292 end
# File lib/rgl/base.rb 262 def eql_graph?(other) 263 other.is_a?(Graph) && directed? == other.directed? && eql_vertices_set?(other) && eql_edges_set?(other) 264 end
# File lib/rgl/base.rb 266 def eql_vertices_set?(other) 267 other_num_vertices = 0 268 269 other.each_vertex do |v| 270 if has_vertex?(v) 271 other_num_vertices += 1 272 else 273 return false 274 end 275 end 276 277 other_num_vertices == num_vertices 278 end