Stress Centrality

Stress centrality (Shimbel 1953) counts the shortest paths between other pairs of nodes that pass through a node: $$S(v) = \sum_{s \ne v \ne t} \sigma_{st}(v),$$ where \(\sigma_{st}(v)\) is the number of shortest paths from \(s\) to \(t\) through \(v\). Betweenness divides each count by the number of shortest paths between the pair; stress keeps the counts.

Usage

centrality_stress(x, ...)

Arguments

x

Network input accepted by centrality.

...

Further arguments to centrality. The measure uses weighted (default TRUE), invert_weights (default NULL, which inverts for tna input only) and alpha (inversion exponent, default 1).

Value

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

Details

Edge weights are read as distances. weighted = FALSE uses hop counts, and invert_weights = TRUE converts a weight \(w\) to the distance \(1/w^\alpha\). On a directed network the paths follow edge direction, and on an undirected network each pair is counted once. The values equal sna::stresscent().

References

Shimbel, A. (1953). Structural parameters of communication networks. The Bulletin of Mathematical Biophysics, 15(4), 501-507. doi:10.1007/BF02476438 .

See also

centrality_betweenness, centrality_load, centrality.

Examples

centrality_stress(regulation_net)
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#>          5         16         19         16         11          1          7 
#>   Evaluate     Create      Share 
#>          3         13         10