L1centNB {L1centrality} | R Documentation |
Derives L1 centrality- or L1 prestige-based neighborhood of each vertex. For undirected graphs, the two neighborhood are identical.
L1centNB(g, eta, mode)
## S3 method for class 'igraph'
L1centNB(g, eta = NULL, mode = c("centrality", "prestige"))
## S3 method for class 'matrix'
L1centNB(g, eta = NULL, mode = c("centrality", "prestige"))
## S3 method for class 'L1centNB'
print(x, ...)
g |
An |
eta |
An optional nonnegative multiplicity (weight) vector for (vertex)
weighted networks. The sum of its components must be positive. If set to
|
mode |
A character string. For an undirected graph, either choice gives the same result.
|
x |
An |
... |
Further arguments passed to or from other methods. This argument is ignored here. |
For an undirected graph, if the graph is symmetrized (in a way defined in Kang and Oh (2024a)) w.r.t. a vertex v, vertex v becomes the graph median (Kang and Oh 2024a), i.e., v has L1 centrality 1. Based on this property, we define the L1 centrality-based neighborhood of vertex v as vertices that have large L1 centrality on the symmetrized graph w.r.t. vertex v.
For a directed graph, a vertex of interest, say v, is made to a centrality and prestige median vertex by the procedure described in Kang and Oh (2024b). We call the resulting graph as the modified graph w.r.t. v. L1 centrality (prestige) -based neighborhood of vertex v is a set of vertices that have large L1 centrality (prestige) on the modified graph w.r.t. vertex v.
L1centNB()
returns an object of class L1centNB
. It
is a list of numeric vectors. The length of the list is
equivalent to the number of vertices in the graph g
, and the names of the
list are vertex names. Each component of the list is a numeric vector whose
length is equivalent to the number of vertices in the graph g
.
Specifically, the i
th component of the list is a vector of the
L1 centrality of each
vertex, for the modified graph g
w.r.t. the i
th vertex (if mode = "centrality"
) or the
L1 prestige of each
vertex, for the modified graph g
w.r.t. the i
th vertex (if mode = "prestige"
).
print.L1centNB()
prints
L1 centrality or
L1 prestige values at
the modified graph w.r.t. each vertex and returns them invisibly.
The function is valid only for connected graphs. If the graph is directed, it must be strongly connected.
S. Kang and H.-S. Oh. On a notion of graph centrality based on L1 data depth. arXiv preprint arXiv:2404.13233, 2024a.
S. Kang and H.-S. Oh. L1 prominence measures for directed graphs. arXiv preprint arXiv:2408.12078, 2024b.
L1cent()
for
L1 centrality/prestige,
L1centLOC()
and L1centEDGE()
internally uses L1centNB()
.
Summary for a relevant summary method.
NB <- L1centNB(MCUmovie, eta = igraph::V(MCUmovie)$worldwidegross)
# Top 6 L1 centrality-based neighbors of "Iron Man"
utils::head(sort(NB$"Iron Man", decreasing = TRUE))