Pairwise Disconnectivity (Potapov et al. 2008)

For a directed network, pairwisedis(v) is the fraction of ordered reachable pairs $(s, t)$ that become unreachable when node $v$ is removed: $$PD(v) = (|P(G)| - |P(G - v)|) / |P(G)|$$ 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: Directed network input (matrix, igraph, cograph_network, tna object).
...: Additional arguments passed to centrality.

Value

Named numeric vector of pairwise disconnectivity values in $[0, 1]$.

Details

Bit-exact match against centiserve::pairwisedis on directed graphs. Requires the input to be directed; returns NA with a warning on undirected inputs.

References

Potapov, A. P., Voss, N., Sasse, N., & Wingender, E. (2008). Topology of mammalian transcription networks. Genome Informatics, 18, 193-204.

Examples

adj <- matrix(c(0,1,0, 0,0,1, 1,0,0), 3, 3, byrow = TRUE)
rownames(adj) <- colnames(adj) <- c("A", "B", "C")
centrality_pairwisedis(adj)
#>         A         B         C 
#> 0.8333333 0.8333333 0.8333333