Communicability Betweenness

Communicability betweenness (Estrada, Higham and Hatano 2009) is the share of the communicability between other pairs of nodes that is lost when the node is removed. With $G = e^{A}$ and $G^{(r)}$ the same exponential after the edges of $r$ are deleted, $$\omega_r = \frac{1}{(n-1)(n-2)} \sum_{p \ne q,\; p, q \ne r} \frac{G_{pq} - G^{(r)}_{pq}}{G_{pq}}.$$

Usage

centrality_communicability_betweenness(x, ...)

Arguments

x: Network input accepted by centrality.
...: Further arguments to centrality, such as directed and normalized.

Value

A named numeric vector with one score per node, in input node order.

Details

$A$ is the binary adjacency matrix, so edge weights are ignored. The scores lie between 0 and 1. The measure is defined for undirected networks. On a directed network $G$ and $G^{(r)}$ are computed by scaling and squaring with a Pade approximation, as in centrality_communicability, so the measure is defined there as well. directed = FALSE gives the undirected reading.

References

Estrada, E., Higham, D. J., & Hatano, N. (2009). Communicability betweenness in complex networks. Physica A, 388(5), 764-774. doi:10.1016/j.physa.2008.11.011 .

Examples

centrality_communicability_betweenness(regulation_net, directed = FALSE)
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#>  0.3148847  0.4393980  0.5536645  0.4284950  0.3108637  0.3278741  0.2334877 
#>   Evaluate     Create      Share 
#>  0.3549724  0.4475289  0.3531491