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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