Coreness Centrality


The coreness centrality, which is estimated with the k-shell indices of the neighbors that are adjacent to a spreader, is a simple but notably powerful indicator to assess the capability of information dissemination through the network. This approach is to consider both the degree and the coreness of a node coincidently by counting the k-shell indices of its neighbor or neighbor of neighbors.
The basic assumption is that a spreader with more connections to the neighbors located in the core of the network is more powerful. Based on this assumption, the neighborhood coreness Cnc of node v is defined as:
Neighborhood Coreness Centrality
where N(v) is the set of the neighbors adjacent to node v and ks(w) is the k-shell index of its neighbor node w. Recursively, the extended neighborhood coreness Cnc+ of node v is defined as follows:
Neighborhood Coreness Centrality
where Cnc(w) is the neighborhood coreness of neighbor w of node v. This observation implies that the extended coreness Cnc+ gives more weights to the coreness than does the neighborhood coreness Cnc.

Once the k-shell index is provided by decomposing the network globally, the coreness centrality can be obtained as a local measure. This feature is significant when we analyze notably large networks or highly dynamic networks.


Unweighted, undirected, and simple networks.

Computational complexity

where m is the number of edges in the network.



  • BAE, J. & KIM, S. 2014. Identifying and ranking influential spreaders in complex networks by neighborhood coreness. Physica A: Statistical Mechanics and its Applications, 395, 549-559. DOI: 10.1016/j.physa.2013.10.047 Publisher web site Endnote RIS file


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