Centralize a graph according to the eigenvector centrality of vertices

See centralize() for a summary of graph centralization.

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.

Examples

# A BA graph is quite centralized
g <- sample_pa(1000, m = 4)
centr_degree(g)$centralization
#> [1] 0.1473045
centr_clo(g, mode = "all")$centralization
#> [1] 0.4057694
centr_betw(g, directed = FALSE)$centralization
#> [1] 0.2188419
centr_eigen(g, directed = FALSE)$centralization
#> [1] 0.9409572

# 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)$centralization
#> [1] 1
centr_eigen(g1)$centralization
#> [1] 0.75

Centralize a graph according to the eigenvector centrality of vertices

Arguments

Value

See also

Related documentation in the C library

Examples