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: the summed gap between the most central node and every other node, divided by the theoretical maximum for the measure, so 0 marks a perfectly even network and 1 a perfect star. Nodes whose score is NA or NaN are dropped from the sum. Returns 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

star <- matrix(0, 5, 5)
star[1, 2:5] <- 1; star[2:5, 1] <- 1
cograph::centralization(star, "degree")
#> [1] 1