The vertex-disjoint k -path centrality is a variant of the \(k\)-path centrality [2], which counts the number of vertex-disjoint paths of length at most \(k\) that originate or terminate at a given node. A vertex-disjoint path is a simple path that shares no nodes with any other counted path, except for the two end nodes. By definition, the set of vertex-disjoint paths is always a subset of the set of edge-disjoint paths. Nodes with higher vertex-disjoint \(k\)-path centrality are therefore more robustly connected, as there are multiple independent paths linking them to other nodes in the network.

References

[1] Shvydun, S. (2025). Zoo of Centralities: Encyclopedia of Node Metrics in Complex Networks. arXiv: 2511.05122 https://doi.org/10.48550/arXiv.2511.05122
[2] Borgatti, S. P., & Everett, M. G. (2006). A graph-theoretic perspective on centrality. Social networks, 28(4), 466-484. doi: 10.1016/j.socnet.2005.11.005.