Residual Closeness Centrality

Residual closeness (Dangalchev 2006) sums distances that decay by half with every step: $$C(i) = \sum_{j} 2^{-d_{ij}},$$ with \(2^{-\infty} = 0\), so the score is defined on disconnected networks.

Usage

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

Arguments

x

Network input accepted by centrality.

mode

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

...

Further arguments to centrality. The measure uses weighted (default TRUE), invert_weights (default NULL, which inverts for tna input only), alpha (inversion exponent, default 1) and cutoff (largest distance counted, default -1 for no limit).

Value

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

Details

The sum includes the node itself, which adds 1, and the values equal centiserve::closeness.residual() on undirected networks. Edge weights are read as distances; weighted = FALSE uses hop counts, and invert_weights = TRUE converts a weight \(w\) to the distance \(1/w^\alpha\). mode = "all" treats edges as undirected, "out" uses distances from the node and "in" distances to it. centrality_dangalchev returns the same values.

References

Dangalchev, C. (2006). Residual closeness in networks. Physica A, 365(2), 556-564. doi:10.1016/j.physa.2005.12.020 .

See also

centrality_dangalchev, centrality_decay, centrality.

Examples

centrality_residual_closeness(regulation_net)
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#>   8.765551   8.592851   8.877387   8.354837   8.781835   8.213449   8.690109 
#>   Evaluate     Create      Share 
#>   8.458391   8.781042   8.238714