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

## Description

communicability calculates the communicability of a network, a measure which takes into account all possible paths (including non-shortest paths) between vertex pairs.

## Usage

 1 communicability(g, weights = NULL) 

## Arguments

 g An igraph graph object weights Numeric vector of edge weights; if NULL (the default), and if the graph has edge attribute weight, then that will be used. To avoid using weights, this should be NA.

## Details

The communicability G_{pq} is a weighted sum of the number of walks from vertex p to q and is calculated by taking the exponential of the adjacency matrix A:

G_{pq} = ∑_{k=0}^{∞} \frac{(\mathbf{A}^k)_{pq}}{k!} = (e^{\mathbf{A}})_{pq}

where k is walk length.

For weighted graphs with D = diag(d_i) a diagonal matrix of vertex strength,

G_{pq} = (e^{\mathbf{D}^{-1/2} \mathbf{A} \mathbf{D}^{-1/2}})_{pq}

## Value

A numeric matrix of the communicability

## Author(s)

Christopher G. Watson, cgwatson@bu.edu

## References

Estrada, E. and Hatano, N. (2008) Communicability in complex networks. Physical Review E. 77, 036111. https://dx.doi.org/10.1103/PhysRevE.77.036111

Crofts, J.J. and Higham, D.J. (2009) A weighted communicability measure applied to complex brain networks. J. R. Soc. Interface. 6, 411–414. https://dx.doi.org/10.1098/rsif.2008.0484

brainGraph documentation built on Oct. 23, 2020, 6:37 p.m.