View source: R/communicability.R
communicability | R Documentation |
communicability
calculates the communicability of a network, a measure
which takes into account all possible paths (including non-shortest paths)
between vertex pairs.
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} = \sum_{k=0}^{\infty} \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. \Sexpr[results=rd]{tools:::Rd_expr_doi("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. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1098/rsif.2008.0484")}
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