Centralization

Centralization of Freeman (1979): how much a network is dominated by its most central node.

Usage

centrality_centralization(
  A,
  measure = c("degree", "closeness", "betweenness", "eigenvector"),
  digraph = FALSE,
  type = c("out", "in", "all"),
  loops = FALSE
)

Arguments

A

A square matrix

measure

The centrality to be used: degree (default), closeness, betweenness or eigenvector

digraph

Whether the matrix is directed or undirected

type

Type of degree or distances for directed networks

loops

Whether to consider the loops of the matrix

Value

This function returns the centralization of the network, the centrality scores and the theoretical maximum.

Details

The centralization is the sum of the differences between the highest centrality and the centrality of every node, divided by the largest sum that a network of the same order can have. For degree, closeness and betweenness the maximum is given by the star network, and for the eigenvector centrality by a network with a single tie, which gives \(n - 2\).

The function is named centrality_centralization() so that it does not mask sna::centralization().

References

Freeman, L. C. (1979). Centrality in social networks conceptual clarification. Social Networks, 1(3), 215–239. doi:10.1016/0378-8733(78)90021-7

Author

Alejandro Espinosa-Rada

Examples

A <- matrix(c(
  0, 1, 1, 1, 0,
  1, 0, 0, 0, 0,
  1, 0, 0, 0, 1,
  1, 0, 0, 0, 0,
  0, 0, 1, 0, 0
), byrow = TRUE, ncol = 5)
rownames(A) <- letters[1:nrow(A)]
colnames(A) <- rownames(A)

centrality_centralization(A, measure = "degree", digraph = FALSE)
#> $centralization
#> [1] 0.5833333
#> 
#> $scores
#> a b c d e 
#> 3 1 2 1 1 
#> 
#> $maximum
#> [1] 12
#> 
centrality_centralization(A, measure = "betweenness", digraph = FALSE)
#> $centralization
#> [1] 0.7083333
#> 
#> $scores
#> a b c d e 
#> 5 0 3 0 0 
#> 
#> $maximum
#> [1] 24
#>