The within-module degree z-score (Guimera and Nunes Amaral 2005) standardizes the number of ties a node has inside its own community against the other members of that community: $$z_i = \frac{\kappa_i - \bar{\kappa}_{s_i}}{\sigma_{\kappa_{s_i}}},$$ where \(\kappa_i\) counts the ties of \(i\) to its community \(s_i\). High values mark hubs within their community.
Arguments
- x
Network input accepted by
centrality.- membership
Community of each node, a vector with one entry per node in input node order (default
NULL).- mode
Direction for directed networks:
"all"(default),"out"or"in".- ...
Further arguments to
centrality.
Details
Edge weights are ignored. mode selects the ties counted, and with
mode = "all" on a directed network a reciprocated tie counts twice.
The standard deviation is the sample value. A community with one member,
or whose members all have the same within-community degree, gives
NaN. Without membership every score is NA with a
warning of classes cograph_bad_membership and
cograph_undefined_measure, and a membership of the wrong
length raises a cograph_bad_membership error. On undirected
networks the values equal
brainGraph::within_module_deg_z_score().
References
Guimera, R., & Nunes Amaral, L. A. (2005). Functional cartography of complex metabolic networks. Nature, 433(7028), 895-900. doi:10.1038/nature03288 .
Examples
centrality_within_module_z(regulation_net, membership = rep(1:2, each = 5))
#> Explore Plan Monitor Adapt Reflect Discuss Synthesize
#> 0.6708204 -1.5652476 0.6708204 -0.4472136 0.6708204 -0.1825742 -1.0954451
#> Evaluate Create Share
#> -0.1825742 1.6431677 -0.1825742