Description Usage Arguments Details Value Author(s) References

View source: R/communicability.R

`communicability`

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

1 | ```
communicability(g, weights = NULL)
``` |

`g` |
An |

`weights` |
Numeric vector of edge weights; if |

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}*

A numeric matrix of the communicability

Christopher G. Watson, cgwatson@bu.edu

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

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