centrality_ehcc: Extended hybrid characteristic centrality

In cograph: Analysis and Visualization of Complex Networks

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, ...)

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.

Value

Named numeric vector in input node order.

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. \Sexpr[results=rd]{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"))

cograph documentation built on Sept. 30, 2026, 5:08 p.m.