Hybrid global structure model centrality

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.

Usage

centrality_hybrid_global_structure(x, ...)

Arguments

x

Network input accepted by centrality.

...

Additional arguments to centrality.

Value

Named numeric vector in input node order.

Details

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.

References

Mukhtar, M. F., et al. (2023). Integrating local and global information to identify influential nodes in complex networks. Scientific Reports, 13, 11411, equations 6-8. doi:10.1038/s41598-023-37570-7 .

Examples

centrality_hybrid_global_structure(igraph::make_ring(4))
#>        1        2        3        4 
#> 16.62538 16.62538 16.62538 16.62538