The gateway coefficient (Ruiz Vargas and Wahl 2014) refines the participation coefficient by weighting the links of node \(i\) into each module \(s\) by how much of the connection between the two modules they carry and by the degree of the neighbors they reach: $$G_i = 1 - \frac{1}{k_i^2} \sum_{s} k_{is}^2 \, g_{is}^2,$$ where \(k_{is}\) is the number of links of \(i\) into module \(s\) and \(g_{is}\) lies between 0 and 1.
Arguments
- x
Network input accepted by
centrality.- membership
Module labels, one per node: integer codes, character labels or a factor.
- mode
For directed networks:
"all"(default),"out"or"in".- ...
Further arguments to
centrality, such asdirectedandnormalized.
Details
Edge weights are ignored, and the score lies between 0 and 1. On a
directed network mode chooses the ties: "out" uses outgoing
links, "in" incoming links and "all" (default) both, with a
reciprocated tie counted twice. The degree \(k_i\), the module
links \(k_{is}\) and the neighbors whose degrees enter
\(g_{is}\) all use the same ties. On an undirected network the
three modes agree and equal brainGraph::gateway_coeff(centr =
"degree"). membership can hold integer, character or factor
labels. Without membership the function returns 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. With a single module
every node scores 0, and so does a node without links in the chosen mode.
References
Ruiz Vargas, E., & Wahl, L. M. (2014). The gateway coefficient: A novel metric for identifying critical connections in modular networks. The European Physical Journal B, 87(7), 161. doi:10.1140/epjb/e2014-40800-7 .
Examples
centrality_gateway(regulation_net, membership = rep(1:2, each = 5))
#> Explore Plan Monitor Adapt Reflect Discuss Synthesize
#> 0.5808315 0.5490589 0.6204854 0.5562922 0.5796028 0.4941561 0.2874009
#> Evaluate Create Share
#> 0.5067149 0.6424167 0.5239164