Mukhtar et al.'s H-GSM (2023) uses \(s_i=\exp(k_s(i)k_i/N)\), \(a=\lceil\log_2(N^{-1}\sum_i s_i)\rceil\), and \(H\text{-}GSM(i)=s_i\sum_{j\ne i}s_j/d_{ij}^{a}\). k_i is simple degree, k_s(i) is original coreness, and d is hop distance. The ceiling exponent is computed from the mean self-influence over ALL original nodes, including isolates whose self-influence is one. The factor s_i alone is not the final centrality score.
centrality_hybrid_global_structure(x, ...)Named numeric vector in input node order.
Network input accepted by centrality.
Additional arguments to centrality.
Topology and disconnected-graph conventions are shared with
centrality_global_structure. The adaptive exponent is
used exactly as specified, including its discontinuities at powers of
two; it is not smoothed or replaced by a fixed exponent.
Self-influence, its mean and final sums are evaluated in logarithmic
form. Raw scores exceeding double precision raise an error. With
normalized = TRUE, final scores are computed directly as
exponentials of log-score differences, so normalized results remain
available even when raw scores overflow. Extremely small normalized
ratios may underflow to zero. Normalization is applied to the complete
score, not separately to self-influence or neighbor contributions.
Mukhtar, M. F., et al. (2023). Integrating local and global information to identify influential nodes in complex networks. Scientific Reports, 13, 11411. tools:::Rd_expr_doi("10.1038/s41598-023-37570-7").
centrality_hybrid_global_structure(igraph::make_ring(4))
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