Information Centrality (Stephenson-Zelen)

Information centrality (Stephenson & Zelen 1989) measures a node's importance in terms of the "information" contained in all paths (not only shortest) passing through it. Defined via the inverse of a Laplacian-like matrix, yielding per-node \(IC_i = 1 / (C_{ii} + (\mathrm{tr}(C) - 2 R_i) / n)\) where \(C = A^{-1}\) and \(R_i\) is the row sum of \(C\).

Usage

centrality_information(x, ...)

Arguments

x: Network input (matrix, igraph, network, cograph_network, tna object).
...: Additional arguments passed to centrality.

Value

Named numeric vector of information centrality values.

Details

Bit-exact match against sna::infocent on connected undirected graphs (cograph mirrors sna's exact construction and call sequence).

References

Stephenson, K., & Zelen, M. (1989). Rethinking centrality: Methods and examples. Social Networks, 11(1), 1-37.

Examples

adj <- matrix(c(0,1,1,0, 1,0,1,1, 1,1,0,1, 0,1,1,0), 4, 4)
rownames(adj) <- colnames(adj) <- LETTERS[1:4]
centrality_information(adj)
#>        A        B        C        D 
#> 1.777778 2.285714 2.285714 1.777778