Centralization index

Computes Freeman's centralization for degree, betweenness, closeness, or eigenvector centrality.

Usage

centralization(
  x,
  measure = c("degree", "betweenness", "closeness", "eigenvector"),
  directed = NULL,
  mode = "all",
  ...
)

Arguments

x

Network input (matrix, edge-list data frame, igraph, network, cograph_network, tna object).

measure

One of "degree" (default), "betweenness", "closeness" or "eigenvector".

directed

Logical or NULL. NULL (default) auto-detects from matrix symmetry; TRUE/FALSE forces it.

mode

For directed networks: "all" (default), "in" or "out". Used by "degree" and "closeness" only.

...

Ignored; accepted for call compatibility with the other centrality verbs.

Value

A single number. It is the summed gap between the most central node and every other node, divided by a theoretical maximum. For degree, betweenness and closeness the maximum is the value of an unweighted star, so unweighted input gives 0 for a perfectly even network and 1 for an undirected star. For eigenvector centrality, whose scores are scaled to a maximum of 1, the divisor is \(n - 1\), and a star gives a value below 1. Weighted closeness scales with the inverse of the edge weights, so its centralization can exceed 1. Nodes whose score is NA or NaN are dropped from the sum. The value is 0 when the network has two or fewer nodes.

Details

A weighted input carries its weights into betweenness, closeness and eigenvector centrality; degree centralization ignores them.

Examples

cograph::centralization(regulation_net, measure = "degree")
#> [1] 0.2469136