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Gil-Schmidt Power Index

Source: R/centrality.R
centrality_gilschmidt.Rd

The Gil-Schmidt power index sums the reciprocal hop distances from a node to the nodes it reaches and divides by \(n - 1\): $$GS(v) = \frac{1}{n - 1} \sum_{w \ne v} \frac{1}{d(v, w)}.$$ Unreachable nodes contribute 0, so the score lies between 0 and 1, and a node adjacent to every other node scores 1.

Usage

centrality_gilschmidt(x, mode = "all", ...)

Arguments

x

Network input accepted by centrality.

mode

For directed networks: "all" (default), "out" or "in".

...

Further arguments to centrality, such as normalized.

Value

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

Details

Distances are hop counts, so edge weights are ignored and invert_weights has no effect. mode sets the direction of the paths. With mode = "out" the values match sna::gilschmidt() with its default settings.

See also

centrality_harmonic, centrality_closeness, centrality.

Examples

centrality_gilschmidt(regulation_net)
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#>  0.7777778  0.8333333  0.8888889  0.8333333  0.7777778  0.7777778  0.7222222 
#>   Evaluate     Create      Share 
#>  0.7777778  0.8333333  0.7777778