brainGraph (version 0.55.0)

part.coeff: Calculate vertex participation coefficient

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. } description{ This function calculates the participation coefficient of each vertex in a graph, based on community membership. } details{ The participation coefficient eqn{P_i} of vertex emph{i} is: deqn{P_i = 1 - sum_{s=1}^{N_M} ( _{is}{_i )^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. } [object Object],[object Object] 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.