eigen_centrality: Find Eigenvector Centrality Scores of Network Positions
Description
eigen_centrality
takes a graph (graph
) and returns the
eigenvector centralities of positions v
within itUsage
eigen_centrality(graph, directed = FALSE, scale = TRUE, weights = NULL,
options = arpack_defaults)
Arguments
graph
Graph to be analyzed.
directed
Logical scalar, whether to consider direction of the edges
in directed graphs. It is ignored for undirected graphs.
scale
Logical scalar, whether to scale the result to have a maximum
score of one. If no scaling is used then the result vector has unit length
in the Euclidean norm.
weights
A numerical vector or NULL
. This argument can be used
to give edge weights for calculating the weighted eigenvector centrality of
vertices. If this is NULL
and the graph has a weight
edge
attribute then that is used.
options
A named list, to override some ARPACK options. See
arpack
for details. Value
- A named list with components:
- vectorA vector containing the
centrality scores.
- valueThe eigenvalue corresponding to the
calculated eigenvector, i.e. the centrality scores.
- optionsA named
list, information about the underlying ARPACK computation. See
arpack
for the details.
WARNING
eigen_centrality
will not symmetrize your data
before extracting eigenvectors; don't send this routine asymmetric matrices
unless you really mean to do so.Details
Eigenvector centrality scores correspond to the values of the first
eigenvector of the graph adjacency matrix; these scores may, in turn, be
interpreted as arising from a reciprocal process in which the centrality of
each actor is proportional to the sum of the centralities of those actors to
whom he or she is connected. In general, vertices with high eigenvector
centralities are those which are connected to many other vertices which are,
in turn, connected to many others (and so on). (The perceptive may realize
that this implies that the largest values will be obtained by individuals in
large cliques (or high-density substructures). This is also intelligible
from an algebraic point of view, with the first eigenvector being closely
related to the best rank-1 approximation of the adjacency matrix (a
relationship which is easy to see in the special case of a diagonalizable
symmetric real matrix via the $SLS^-1$
decomposition).)From igraph version 0.5 this function uses ARPACK for the underlying
computation, see arpack
for more about ARPACK in igraph.
References
Bonacich, P. (1987). Power and Centrality: A Family of
Measures. American Journal of Sociology, 92, 1170-1182.Examples
Run this code#Generate some test data
g <- make_ring(10, directed=FALSE)
#Compute eigenvector centrality scores
eigen_centrality(g)
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