centrality_adaptive_leaderrank: Adaptive LeaderRank centrality

In cograph: Analysis and Visualization of Complex Networks

Adaptive LeaderRank centrality

Description

Xu and Wang's adaptive LeaderRank computes original node H-indices, then adds a ground node with H-index one, joined bidirectionally to every original node. Each augmented arc from j to i has weight a_{ji}h_i. Row-normalized weights define the resource transition matrix. Raw stationary scores retain total augmented mass N, following initial score one on ordinary nodes and zero on ground. The ground score is omitted without redistribution. H-indices are not recomputed after ground edges are added.

Usage

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

Arguments

x	Network input accepted by centrality.
alr_h_mode	Original H-index convention: all (default), out or in.
...	Additional arguments to centrality.

Details

The H-index is the largest integer h for which at least h original neighbors have degree at least h. The focal node is excluded from that neighbor list. This differs from cograph's existing closed-neighborhood centrality_lobby convention.

The paper evaluates directed and undirected networks but does not pin a directed H-index convention. alr_h_mode makes that choice explicit. Default "all" computes H-indices on the simple undirected skeleton, merging reciprocal arcs. "out" uses outgoing neighbors' out-degrees; "in" uses incoming neighbors' in-degrees. These directed H-index choices are explicit cograph conventions, not claims of the authors' directed-software behavior. In every case, resource flow retains the original directed arcs. Undirected edges become opposite arcs, and all H-index modes then coincide.

Input weights are ignored; the algorithm generates its own destination weights. Loops are removed and parallel arcs count once. The generic mode, inversion and cutoff arguments are ignored. Original nodes with H-index zero receive zero stationary score. If every H-index is zero, the ground transition row is undefined and all scores are NaN. This can occur on edgeless inputs or some directed inputs in in/out H-index modes. Empty input returns an empty vector. No H-index pseudocount is added.

A native ground-elimination solve obtains the unique stationary solution in O(N^3) time and O(N^2) memory, including periodic chains for which ordinary iteration need not converge. Optional final max normalization acts on the returned ordinary-node scores. Numerical definition agreement does not establish superior spreading predictions or author-code parity.

Value

Named numeric vector in input node order.

References

Xu, S., & Wang, P. (2017). Identifying important nodes by adaptive LeaderRank. Physica A, 469, 654-664. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.physa.2016.11.034")}.

Examples

centrality_adaptive_leaderrank(igraph::make_ring(4))

cograph documentation built on Sept. 30, 2026, 5:08 p.m.