Extended Hybrid Characteristic Centrality

Extended hybrid characteristic centrality (Liu and Zheng 2023) adds to a node's centrality_hcc score the scores of its neighbors. $$EHCC(u) = HCC(u) + \sum_{v \in \phi(u)} HCC(v)$$

Usage

centrality_ehcc(x, ...)

Arguments

x: Network input accepted by centrality.
...: Further arguments to centrality. The measure uses hcc_delta (weight $\delta$ of the node's own degree in the extended degree, default 0.5).

Value

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

Details

The measure inherits the conventions of centrality_hcc. It is computed on the simple undirected skeleton, so direction, weights, loops and parallel edges are ignored, and a hcc_delta outside $[0, 1]$ raises a cograph_bad_parameter error. Scores lie in $[0, 2(1 + k_{max})]$, and an isolate scores its own HCC.

References

Liu, J. and Zheng, J. (2023). Identifying important nodes in complex networks based on extended degree and E-shell hierarchy decomposition. Scientific Reports, 13, 3197. doi:10.1038/s41598-023-30308-5 .

Examples

centrality_ehcc(regulation_net)
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#>   8.537879  11.060606  12.356061  10.045455   7.946970   8.772727   7.212121 
#>   Evaluate     Create      Share 
#>   9.924242  11.484848  10.113636