igraph (version 1.0.0)

centr_eigen: 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 = TRUE,
  options = arpack_defaults, normalized = TRUE)

Arguments

graph

The input graph.

directed

logical scalar, whether to use directed shortest paths for calculating eigenvector centrality.

scale

Whether to rescale the eigenvector centrality scores, such that the maximum score is one.

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.

See Also

Other centralization related: centr_betw_tmax, centralization.betweenness.tmax; centr_betw, centralization.betweenness; centr_clo_tmax, centralization.closeness.tmax; centr_clo, centralization.closeness; centr_degree_tmax, centralization.degree.tmax; centr_degree, centralization.degree; centr_eigen_tmax, centralization.evcent.tmax; centralization, centralize, centralize.scores

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