View source: R/neighborhood.inclusion.R
neighborhood_inclusion | R Documentation |
Calculates the neighborhood-inclusion preorder of an undirected graph.
neighborhood_inclusion(g, sparse = FALSE)
g |
An igraph object |
sparse |
Logical scalar, whether to create a sparse matrix |
Neighborhood-inclusion is defined as
N(u)\subseteq N[v]
where N(u)
is the neighborhood of u
and N[v]=N(v)\cup \lbrace v\rbrace
is the closed neighborhood of v
.
N(u) \subseteq N[v]
implies that c(u) \leq c(v)
,
where c
is a centrality index based on a specific path algebra. Indices
falling into this category are closeness (and variants), betweenness
(and variants) as well as many walk-based indices (eigenvector and subgraph
centrality, total communicability,...).
The neighborhood-inclusion preorder of g
as matrix object. P[u,v]=1
if N(u)\subseteq N[v]
David Schoch
Schoch, D. and Brandes, U., 2016. Re-conceptualizing centrality in social networks. European Journal of Applied Mathematics 27(6), 971-985.
Brandes, U. Heine, M., Müller, J. and Ortmann, M., 2017. Positional Dominance: Concepts and Algorithms. Conference on Algorithms and Discrete Applied Mathematics, 60-71.
positional_dominance, exact_rank_prob
library(igraph)
# the neighborhood inclusion preorder of a star graph is complete
g <- graph.star(5, "undirected")
P <- neighborhood_inclusion(g)
comparable_pairs(P)
# the same holds for threshold graphs
tg <- threshold_graph(50, 0.1)
P <- neighborhood_inclusion(tg)
comparable_pairs(P)
# standard centrality indices preserve neighborhood-inclusion
data("dbces11")
P <- neighborhood_inclusion(dbces11)
is_preserved(P, degree(dbces11))
is_preserved(P, closeness(dbces11))
is_preserved(P, betweenness(dbces11))
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