Improved Global Structure Model Centrality

The improved global structure model (IGSM; Zhu and Wang 2022) replaces the core numbers of centrality_global_structure with degrees and raises each distance to an exponent set by the mean degree $\bar{k}$: $$IGSM(i) = \exp\left(\frac{k_i}{N}\right) \sum_{j \ne i} \frac{k_j}{d_{ij}^{a}}, \qquad a = \lceil \log_2 \bar{k} \rceil.$$ The formula follows equation 5 of Mukhtar et al. (2023).

Usage

centrality_improved_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, and $N$ and the mean degree include every node of the network. When the mean degree is at most 1 the exponent is zero or negative, and with a negative exponent distant nodes contribute more than near ones. An isolated node scores 0, and so does every node of a network without edges.

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 .

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_improved_global_structure(regulation_net)
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#>   49.04946   61.95204   77.02604   60.35769   47.60683   50.49209   40.65222 
#>   Evaluate     Create      Share 
#>   53.37735   63.54639   53.37735