Pairwise Disconnectivity

Pairwise disconnectivity (Potapov et al. 2008) is the share of ordered reachable pairs that become unreachable when a node is removed: $$PD(v) = \frac{|P(G)| - |P(G - v)|}{|P(G)|},$$ where \(|P(G)|\) is the number of ordered pairs \((s, t)\), \(s \ne t\), with a directed path from \(s\) to \(t\).

Usage

centrality_pairwisedis(x, ...)

Arguments

x

Network input accepted by centrality.

...

Further arguments to centrality.

Value

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

Details

The measure needs a directed network. On undirected input every score is NA with a cograph_undefined_measure warning. Reachability uses hop counts, so edge weights are ignored. The score lies between 0 and 1, and a network without reachable pairs scores 0 everywhere. The values equal centiserve::pairwisedis().

References

Potapov, A. P., Goemann, B., & Wingender, E. (2008). The pairwise disconnectivity index as a new metric for the topological analysis of regulatory networks. BMC Bioinformatics, 9, 227. doi:10.1186/1471-2105-9-227 .

See also

centrality_prestige_domain, robustness, centrality.

Examples

centrality_pairwisedis(regulation_net)
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#>  0.2000000  0.2000000  0.2000000  0.2888889  0.2000000  0.2000000  0.2000000 
#>   Evaluate     Create      Share 
#>  0.2000000  0.2000000  0.2000000