Participation Coefficient

The participation coefficient (Guimera and Nunes Amaral 2005) measures how evenly the ties of a node spread over communities: $$P_i = 1 - \sum_{s} \left(\frac{k_{is}}{k_i}\right)^2,$$ where $k_{is}$ counts the ties of node $i$ to community $s$ and $k_i$ is its degree.

Usage

centrality_participation(x, membership = NULL, mode = "all", ...)

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.

Value

A named numeric vector with one score per node, in input node order.

Details

Edge weights are ignored. mode selects the ties counted, and with mode = "all" on a directed network a reciprocated tie counts twice. A node whose ties all stay in one community scores 0, as does an isolated node, and the score is below 1. 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::part_coeff().

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_participation(regulation_net, membership = rep(1:2, each = 5))
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#>  0.5000000  0.2448980  0.4687500  0.4444444  0.5000000  0.3200000  0.0000000 
#>   Evaluate     Create      Share 
#>  0.3200000  0.4897959  0.2777778