Random Walk Centrality

Random walk centrality is the inverse of the summed random-walk distances from a node to the others: $$RW(i) = \left(\sum_{j} \frac{m_{ij} + m_{ji}}{2}\right)^{-1},$$ where \(m_{ij}\) is the mean first passage time from \(i\) to \(j\) of a walk that moves to each out-neighbor with equal probability.

Usage

centrality_random_walk(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

Edge weights are ignored. The measure is defined for connected undirected and strongly connected directed networks. On any other network every score is NA, with a cograph_undefined_measure warning, because some passage times are infinite. The passage times are symmetrized before the sum, so the values differ from tidygraph::centrality_random_walk(), which sums them unsymmetrized.

See also

centrality_markov, centrality_current_flow_closeness, centrality.

Examples

centrality_random_walk(regulation_net)
#>     Explore        Plan     Monitor       Adapt     Reflect     Discuss 
#> 0.012216636 0.008002654 0.013333103 0.012968861 0.011194826 0.008290386 
#>  Synthesize    Evaluate      Create       Share 
#> 0.007141018 0.006606541 0.011334481 0.011743819