# centr_betw_comm: Calculate communicability betweenness centrality In brainGraph: Graph Theory Analysis of Brain MRI Data

## Description

centr_betw_comm calculates the communicability betweenness of the vertices of a graph. The centrality for vertex r is

ω_r = \frac{1}{C} ∑_p ∑_q \frac{(e^{\mathbf{A}})_{pq} - (e^{\mathbf{A} + \mathbf{E}(r)})_{pq}}{(e^{\mathbf{A}})_{pq}}

where C = (n - 1)^2 - (n - 1) is a normalization factor.

## Usage

 1 centr_betw_comm(g, A = NULL) 

## Arguments

 g An igraph graph object A Numeric matrix; the adjacency matrix of the input graph. Default: NULL

## Value

A numeric vector of the centrality for each vertex

## Author(s)

Christopher G. Watson, cgwatson@bu.edu

## References

Estrada, E. and Higham, D.J. and Hatano N. (2009) Communicability betweenness in complex networks. Physica A, 388, 764–774. https://dx.doi.org/10.1016/j.physa.2008.11.011

Other Centrality functions: centr_lev