cograph (version 2.7.2)

centrality_ehcc: Extended hybrid characteristic centrality

Description

The extended hybrid characteristic centrality of Liu and Zheng is the closed-neighborhood sum of centrality_hcc: \(EHCC(u)=HCC(u)+\sum_{v\in\phi(u)}HCC(v)\), the focal node counted once and each neighbor of the open 1-order neighborhood once. It rewards a node whose neighbors are themselves high in both the extended degree and the E-shell hierarchy, which a node can be without being high itself.

Usage

centrality_ehcc(x, ...)

Value

Named numeric vector in input node order.

Arguments

x

Network input accepted by centrality.

...

Additional arguments to centrality, including hcc_delta.

Details

Everything recorded on centrality_hcc carries over unchanged: the source's \(\arg\max\)/\(\arg\min\) typo in step 3 of the E-shell procedure, the original-graph reading of \(k^{ex}\) and \(k^{ex}_{max}\) against the residual-graph peel, the global and therefore not component-local normalizers, the hcc_delta domain \([0,1]\), the \(0/0\) of an edgeless graph written as zero, the simple undirected unweighted skeleton, and the ignored weights, mode, cutoff and inversion. Because HCC lies in \([0,2]\), EHCC lies in \([0,2(1+k_{max})]\), and an isolate scores exactly 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. tools:::Rd_expr_doi("10.1038/s41598-023-30308-5").

See Also

centrality_hcc for the summand and list_centralities for the catalogue.

Examples

# On a regular graph every node scores 2, so EHCC is 2 (1 + k).
centrality_ehcc(igraph::make_ring(6))

# The star's center collects every leaf's score as well as its own.
centrality_ehcc(igraph::make_star(6, mode = "undirected"))