communibet {centiserve} | R Documentation |
The communicability betweenness of a node r is:
omega(r) = 1/C * sum(sum(G(prq)/G(pq), q), p), p!=q,p!=r,q!=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.
communibet(graph, vids = V(graph), normalized = FALSE)
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. |
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
A numeric vector contaning the centrality scores for the selected vertices.
Mahdi Jalili m_jalili@farabi.tums.ac.ir
Algorithm adapted from NetworkX 1.9 (Hagberg, A. 2008).
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.
## 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)