Hybrid Global Structure Model Centrality

The hybrid global structure model (H-GSM; Mukhtar et al. 2023) combines a self-influence $s_i = \exp(k_s(i)\, k_i / N)$ with a distance exponent $a$ computed from the mean self-influence: $$HGSM(i) = s_i \sum_{j \ne i} \frac{s_j}{d_{ij}^{a}}, \qquad a = \left\lceil \log_2 \frac{1}{N} \sum_l s_l \right\rceil.$$ Here $k_s(i)$ is the core number, $k_i$ the degree and $N$ the number of nodes, isolated nodes included.

Usage

centrality_hybrid_global_structure(x, ...)

Arguments

x: Network input accepted by centrality.
...: Further arguments to centrality, such as normalized.

Value

A named numeric vector with one score per node, in input node order.

Details

The measure uses the simple undirected skeleton, so direction, weights, loops and parallel edges are ignored, and mode has no effect. Only reachable nodes contribute to the sum. Other components affect the scores through $N$ and the mean self-influence, to which each isolated node adds 1. An isolated node scores 0. Raw scores beyond double precision raise an error. With normalized = TRUE the scores are computed on the log scale and remain available in that case.

References

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

Examples

centrality_hybrid_global_structure(regulation_net)
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#>   345.0810   619.5092  1004.9876   581.9533   340.5875   370.2555   239.8073 
#>   Evaluate     Create      Share 
#>   432.9857   644.6836   432.9857