Adaptive LeaderRank

Adaptive LeaderRank (Xu and Wang 2017) adds a ground node with H-index 1 that is linked in both directions to every node, and weights each arc from \(j\) to \(i\) by the H-index \(h_i\) of its target. The H-index of a node is the largest \(h\) such that at least \(h\) of its neighbors have degree at least \(h\). The score is the stationary resource of the random walk on the row-normalized weights, started with one unit on every node and none on the ground.

Usage

centrality_adaptive_leaderrank(x, alr_h_mode = "all", ...)

Arguments

x: Network input accepted by centrality.
alr_h_mode: Neighbors and degrees used for the H-index: "all" (default), "out" or "in". On an undirected network the three agree.
...: Further arguments to centrality, such as normalized.

Value

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

Details

The random walk keeps the direction of the arcs, and an undirected edge counts as two opposite arcs. Edge weights, loops and parallel arcs are ignored, and mode has no effect. H-indices are computed once on the original network. With alr_h_mode = "all" they use the simple undirected skeleton, "out" uses the out-degrees of out-neighbors and "in" the in-degrees of in-neighbors. The returned scores omit the ground, so they sum to less than \(N\). A node with H-index 0 scores 0, and when every H-index is 0 all scores are NaN with a cograph_undefined_measure warning.

References

Xu, S., & Wang, P. (2017). Identifying important nodes by adaptive LeaderRank. Physica A, 469, 654-664. doi:10.1016/j.physa.2016.11.034 .

Examples

centrality_adaptive_leaderrank(regulation_net)
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#>  1.3925921  0.5545210  1.5092781  1.2537922  0.9927462  0.5961666  0.3916223 
#>   Evaluate     Create      Share 
#>  0.4313295  1.0629935  1.1276256