Global Structure Model Centrality

The global structure model (GSM; Ullah et al. 2021) multiplies a coreness factor of the node by the coreness of all other nodes, each discounted by its hop distance: $$GSM(i) = \exp\left(\frac{k_s(i)}{N}\right) \sum_{j \ne i} \frac{k_s(j)}{d_{ij}}.$$ Here $k_s$ is the core number and $N$ the number of nodes, isolated nodes included.

Usage

centrality_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, which extends the measure to disconnected networks. Other components still affect the scores through $N$. An isolated node scores 0.

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. doi:10.1038/s41598-021-84684-x .

Examples

centrality_global_structure(regulation_net)
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#>   41.77109   44.75474   47.73839   44.75474   41.77109   41.77109   38.78744 
#>   Evaluate     Create      Share 
#>   41.77109   44.75474   41.77109