The Global Structure Model (GSM) of Ullah et al. (2021) is \(GSM(i)=\exp(k_s(i)/N)\sum_{j\ne i}k_s(j)/d_{ij}\), where k_s denotes original graph core numbers and d denotes hop distances. It combines a focal coreness factor with distance-discounted coreness of other nodes. N is the total original node count, including isolates.
Arguments
- x
Network input accepted by
centrality.- ...
Additional arguments to
centrality.normalized = TRUEdivides final scores by their maximum.
Details
Both GSM and centrality_hybrid_global_structure use the
simple undirected skeleton, ignoring weights, mode, path inversion and
distance cutoffs. Loops are removed and parallel connections count once.
Only reachable partners contribute; this is an explicit disconnected-graph
extension. Isolates and singletons score zero, empty input returns an
empty vector. Other components can affect results through the global
node count and, for H-GSM, its global mean. These are not independent
per-component calculations.
Production uses native coreness and all-pairs distance kernels, with worst-case O(N^3) time and O(N^2) memory. Numerical verification uses independent NetworkX cores/distances and exhaustive small-graph oracles. Agreement with a numerical definition does not establish author-software parity or superior epidemic-spreading predictions.
References
Ullah, A., Wang, B., Sheng, J., Long, J., Khan, N., & Sun, Z. (2021). Identification of nodes influence based on global structure model in complex networks. Scientific Reports, 11, 6173, equations 5-8. doi:10.1038/s41598-021-84684-x .
Examples
centrality_global_structure(igraph::make_ring(4))
#> 1 2 3 4
#> 8.243606 8.243606 8.243606 8.243606