| communibet {centiserve} | R Documentation |
Find the communicability betweenness centrality
Description
The communicability betweenness of a node r is:
\omega_{r} = \frac{1}{C} \sum_{p}\sum_{q}\frac{G_{prq}}{G_{pq}}, p\neq q,p\neq r, q\neq r
where where G_{prq} = (e^{A})_{pq} - (e^{A+E(r)})_{pq} is the number of walks involving node r, G_{pq} = (e^{A})_{pq} is the number of closed walks starting at node p and ending at node q, and C = (n-1)^{2}-(n-1) is a normalization factor equal to the number of terms in the sum.
Usage
communibet(graph, vids = V(graph), normalized = FALSE)
Arguments
graph |
The input graph as igraph object |
vids |
Vertex sequence, the vertices for which the centrality values are returned. Default is all vertices. |
normalized |
Logical scalar, whether to calculate the normalized score. |
Details
Communicability betweenness measure makes use of the number of walks connecting every pair of nodes as the basis of a betweenness centrality measure.
The resulting \omega_{r} takes values between zero and one. The lower bound cannot be attained for a connected graph, and the upper bound is attained in the star graph.
More detail at Communicability Betweenness Centrality
Value
A numeric vector contaning the centrality scores for the selected vertices.
Author(s)
Mahdi Jalili m_jalili@farabi.tums.ac.ir
Algorithm adapted from NetworkX 1.9 (Hagberg, A. 2008).
References
Estrada, Ernesto, Desmond J. Higham, and Naomichi Hatano. "Communicability betweenness in complex networks." Physica A: Statistical Mechanics and its Applications 388.5 (2009): 764-774.
Hagberg, Aric, Pieter Swart, and Daniel S Chult. Exploring network structure, dynamics, and function using NetworkX. No. LA-UR-08-05495; LA-UR-08-5495. Los Alamos National Laboratory (LANL), 2008.
Examples
## Not run:
g <- graph(c(1,2,2,3,2,6,6,5,3,5,3,4,5,4,4,7), directed=FALSE)
communibet(g)
## End(Not run)