Closeness Vitality

Closeness vitality (Koschuetzki et al. 2005) is the drop in the Wiener index when a node is removed: $$CV(v) = W(G) - W(G - v), \qquad W(G) = \sum_{s \ne t} d(s, t).$$ The Wiener index sums the finite distances over ordered pairs, as in networkx::closeness_vitality().

Usage

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

Arguments

x

Network input accepted by centrality.

mode

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

...

Further arguments to centrality. The measure uses weighted (default TRUE), invert_weights (default NULL, which is TRUE for tna input), alpha (inversion exponent, default 1) and cutoff (largest path length considered, default -1 for no limit).

Value

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

Details

Edge weights are read as path lengths. invert_weights = TRUE uses \(1/w^\alpha\) as the length, and weighted = FALSE counts hops. mode sets the direction of the paths. Pairs that are not connected contribute nothing to either index. An isolated node scores 0.

References

Koschuetzki, D., Lehmann, K. A., Peeters, L., Richter, S., Tenfelde-Podehl, D., & Zlotowski, O. (2005). Centrality indices. In U. Brandes & T. Erlebach (Eds.), Network Analysis: Methodological Foundations (pp. 16-61). Springer. doi:10.1007/978-3-540-31955-9_3 .

See also

centrality_wiener, centrality_centroid, centrality.

Examples

centrality_closeness_vitality(regulation_net)
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#>       2.60       4.04       1.34       5.28       0.82       5.78       4.12 
#>   Evaluate     Create      Share 
#>       4.96       2.52       5.68