Two-Way Random Walk Betweenness

Two-way random walk betweenness (Curado et al. 2022) counts how often a node lies on the strongest two-way route between a pair. For every unordered pair \((i, j)\) the two-step transfer \(P_{itj} = w_{it} w_{tj} / (d_i d_j)\) is combined into \(T_{ij}[t, k] = P_{itj} P_{jki}\), the diagonal is dropped, and the largest entry credits one count to \(t\) and one to \(k\). The score of a node is its total count over all pairs.

Usage

centrality_two_way_rw(x, ...)

Arguments

x: Network input accepted by centrality.
...: Further arguments to centrality. The measure uses weighted (use edge weights, default TRUE).

Value

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

Details

Edge weights are used, and direction and self-loops are ignored. Ties in the maximum go to the first entry in row-major order. Nodes that never lie on a winning two-way route score 0. The source divides the transfer by \(d_i d_j\), where a random-walk probability would divide by \(d_i d_t\). The formula is implemented as printed.

References

Curado, M., Rodriguez, R., Tortosa, L., & Vicent, J. F. (2022). A new centrality measure in dense networks based on two-way random walk betweenness. Applied Mathematics and Computation, 412, 126560.

Examples

centrality_two_way_rw(regulation_net)
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#>          5          9          8         14          6          5          2 
#>   Evaluate     Create      Share 
#>          7          6         10