Extended Neighborhood Coreness

Extended neighborhood coreness (Bae and Kim 2014) sums the neighborhood coreness of every neighbor of a node: $$C_{nc+}(i) = \sum_{j \in N(i)} \sum_{l \in N(j)} k_s(l),$$ where \(k_s\) is the core number in the whole network. The score equals \(A^2 k_s\).

Usage

centrality_extended_coreness(x, ...)

Arguments

x

Network input accepted by centrality.

...

Further arguments to centrality, such as normalized.

Value

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

Details

The measure uses the simple undirected skeleton, so direction, weights, loops and parallel edges are ignored. Every walk of length two adds the core number of its endpoint, including walks that return to the focal node. Isolated nodes score 0. On a tree the score equals the sum of the neighbors' degrees, and on a \(d\)-regular network it equals \(d^3\).

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 .

See also

centrality_coreness, centrality_extended_gravity, centrality.

Examples

centrality_extended_coreness(regulation_net)
#>    Explore       Plan    Monitor      Adapt    Reflect    Discuss Synthesize 
#>        108        128        148        124        104        112         96 
#>   Evaluate     Create      Share 
#>        120        132        120