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.
Arguments
- x
Network input accepted by
centrality.- ...
Additional arguments to
centrality. Withnormalized = 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.
References
Bae, J., & Kim, S. (2014). Identifying and ranking influential spreaders in complex networks by neighborhood coreness. Physica A, 395, 549-559. doi:10.1016/j.physa.2013.10.047 . The equations used here are reproduced as equations 2 and 3 in Ma, Ma, Zhang & Wang (2016), Physica A, 451, 205-212. doi:10.1016/j.physa.2015.12.162 .
Examples
centrality_extended_coreness(igraph::make_ring(6))
#> 1 2 3 4 5 6
#> 8 8 8 8 8 8