centrality_extended_coreness: Extended neighborhood coreness

In cograph: Analysis and Visualization of Complex Networks

Extended neighborhood coreness

Description

Bae and Kim's extended neighborhood coreness sums the neighborhood coreness of every immediate neighbor: C_{nc+}(i)=\sum_{j\in N(i)}\sum_{l\in N(j)}k_s(l). Equivalently, the score is A^2 k_s. Here k_s is the core-number vector of the original simple undirected graph. Core numbers are not recomputed inside each neighborhood.

Usage

centrality_extended_coreness(x, ...)

Arguments

x	Network input accepted by centrality.
...	Additional arguments to centrality. With normalized = TRUE, positive scores are divided by their maximum.

Details

Every length-two walk contributes its endpoint's core number, including returns to the focal node and repeated endpoints reached via different neighbors. This is not a sum over distinct nodes at distance two. Isolates score zero. On a tree, it equals the sum of neighboring degrees; on a d-regular graph it equals d cubed. A larger score means more access to core-rich neighborhoods; numerical equivalence does not imply superior spreading prediction for every network.

Uses the simple undirected unweighted skeleton: either direction creates an edge, parallel edges count once and loops are removed. This projection is a cograph convention for inputs outside the published domain. Weights, mode and shortest-path weight inversion do not affect the score.

Value

Named numeric vector in input node order.

References

Bae, J., & Kim, S. (2014). Identifying and ranking influential spreaders in complex networks by neighborhood coreness. Physica A, 395, 549-559. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.physa.2013.10.047")}.

Examples

centrality_extended_coreness(igraph::make_ring(6))

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