centr_eigen: Centralize a graph according to the eigenvector centrality of...

In igraph: Network Analysis and Visualization

Centralize a graph according to the eigenvector centrality of vertices

Description

See centralize() for a summary of graph centralization.

Usage

centr_eigen(
  graph,
  directed = FALSE,
  scale = deprecated(),
  options = arpack_defaults(),
  normalized = TRUE
)

Arguments

graph	The input graph.
directed	logical scalar, whether to use directed shortest paths for calculating eigenvector centrality.
scale	Ignored. Computing eigenvector centralization requires normalized eigenvector centrality scores.
options	This is passed to eigen_centrality(), the options for the ARPACK eigensolver.
normalized	Logical scalar. Whether to normalize the graph level centrality score by dividing by the theoretical maximum.

Value

A named list with the following components:

vector

The node-level centrality scores.

value

The corresponding eigenvalue.

options

ARPACK options, see the return value of eigen_centrality() for details.

centralization

The graph level centrality index.

theoretical_max

The same as above, the theoretical maximum centralization score for a graph with the same number of vertices.

Related documentation in the C library

centralization_eigenvector_centrality().

See Also

Other centralization related: centr_betw(), centr_betw_tmax(), centr_clo(), centr_clo_tmax(), centr_degree(), centr_degree_tmax(), centr_eigen_tmax(), centralize()

Examples

# A BA graph is quite centralized
g <- sample_pa(1000, m = 4)
centr_degree(g)$centralization
centr_clo(g, mode = "all")$centralization
centr_betw(g, directed = FALSE)$centralization
centr_eigen(g, directed = FALSE)$centralization

# The most centralized graph according to eigenvector centrality
g0 <- make_graph(c(2, 1), n = 10, dir = FALSE)
g1 <- make_star(10, mode = "undirected")
centr_eigen(g0)$centralization
centr_eigen(g1)$centralization

igraph documentation built on Feb. 12, 2026, 5:08 p.m.