Improved global structure model centrality — centrality_improved_global

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.

Usage

centrality_improved_global_structure(x, ...)

Arguments

x: Network input accepted by centrality.
...: Additional arguments to centrality.

Value

Named numeric vector in input node order.

Details

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.

References

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. doi:10.1088/1674-1056/ac380d . The implemented IGSM formula is reproduced as equation 5 in Mukhtar et al. (2023), doi:10.1038/s41598-023-37570-7 .

Examples

centrality_improved_global_structure(igraph::make_ring(4))
#>        1        2        3        4 
#> 8.243606 8.243606 8.243606 8.243606