This function calculates the within-module degree z-score of each vertex in a
graph, based on some module membership. This is a measure of the connectivity
from a given vertex to other vertices in its module.
Usage
within_module_deg_z_score(g, memb)
Arguments
g
The graph
memb
The community membership indices of each vertex
Value
A vector of the within-module degree z-scores for each vertex of the
graph.
Details
The within-module degree z-score is:
$$z_i = \frac{\kappa_i - \bar{\kappa}_{s_i}}{\sigma_{\kappa_{s_i}}}$$
where $\kappa_i$ is the number of edges from vertex i to vertices
in the same module $s_i$, $\bar{\kappa}_{s_i}$ is the average of
$\kappa$ over all vertices in $s_i$, and $\sigma_{\kappa_{s_i}}$
is the standard deviation.
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.