communibet {centiserve} R Documentation

## Find the communicability betweenness centrality

### Description

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.

### 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)
```

[Package centiserve version 1.0.0 Index]