Weighted LeaderRank (Li et al. 2014) adds a ground node \(g\) that is linked in both directions to every node. Each original arc and each arc into the ground has weight 1, and the arc from the ground to node \(i\) has weight \((k_i^{in})^{\alpha}\), where \(k_i^{in}\) is the in-degree before the ground is added. The score is the stationary resource of the random walk on the row-normalized weights, started with one unit on every node and the ground included.
Arguments
- x
Network input accepted by
centrality.- wlr_alpha
Exponent \(\alpha\) of the in-degree, a finite number. Default 1, one of the values studied by Li et al. (2014).
- ...
Further arguments to
centrality, such asnormalized.
Details
Arcs keep their direction, and an undirected edge counts as two opposite
arcs. Edge weights, loops and parallel arcs are ignored, and mode
has no effect. The returned scores omit the ground, so they sum to less
than \(N+1\). With \(\alpha = 0\) every ground arc
has weight 1. With a positive \(\alpha\) a node with in-degree
0 scores 0, and when every in-degree is 0 all scores are NaN
with a cograph_undefined_measure warning. A negative
\(\alpha\) requires a positive in-degree at every node and
raises a cograph_bad_parameter error otherwise, as does a
wlr_alpha that is not a finite number.
References
Li, Q., Zhou, T., Lu, L., & Chen, D. (2014). Identifying influential spreaders by weighted LeaderRank. Physica A, 404, 47-55. doi:10.1016/j.physa.2014.02.041 .