The IGSM definition reproduced in Mukhtar et al. (2023), equation 5, is \(IGSM(i)=\exp(k_i/N)\sum_{j\ne i}k_j/d_{ij}^{a}\), with \(a=\lceil\log_2(\overline{k})\rceil\). The original method is attributed to Zhu and Wang (2022); the exact equation used here was checked in the later primary experimental paper, not its original full text. IGSM uses simple degrees rather than GSM's core numbers, and its distance exponent depends on global mean degree, including isolates.
centrality_improved_global_structure(x, ...)Named numeric vector in input node order.
Network input accepted by centrality.
Additional arguments to centrality.
Topology, normalization and disconnected-graph conventions follow
centrality_global_structure. For a positive mean degree
below one, the exponent may be zero or negative; it is not clamped.
With a negative exponent, more distant reachable partners contribute
more, an explicit consequence of extending the equation to sparse
disconnected inputs. Unreachable partners still contribute zero.
Edgeless graphs score zero by an explicit extension because the
logarithm of zero in the exponent is otherwise undefined.
This implements IGSM itself, without an additional nearest-neighbor aggregation for the extended IGSM variant.
Zhu, J.-C., & Wang, L.-W. (2022). An extended improved global structure model for influential node identification in complex networks. Chinese Physics B, 31, 068904. tools:::Rd_expr_doi("10.1088/1674-1056/ac380d").
centrality_improved_global_structure(igraph::make_ring(4))
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