This function calculates the participation coefficient of each vertex in a
graph, based on community membership.
Usage
part.coeff(g, memb)
Arguments
g
The graph
memb
The community membership indices of each vertex
Value
A vector of the participation coeff's for each vertex of the graph.
Details
The participation coefficient $P_i$ of vertex i is:
$$P_i = 1 - \sum_{s=1}^{N_M} \left ( \frac{\kappa_{is}}{\kappa_i} \right )^2$$
where $\kappa_{is}$ is the number of edges from vertex i to
vertices in module s, and $\kappa_s$ is the degree of vertex
i. $N_M$ equals the number of modules.
As discussed in Guimera et al., $P_i = 0$ if vertex i is connected
only to vertices in the same module, and $P_i = 1$ if vertex i is
equally connected to all other modules.
References
Guimera, R. and Amaral, L.A.N. (2005) Cartography of complex
networks: modules and universal roles, Journal of Statistical Mechanics:
Theory and Experiment, 02, P02001.