The edge-disjoint k -path centrality is a variant of the k -path centrality [2]. Unlike the original measure, which counts all simple paths, this centrality considers only edge-disjoint paths of length up to \(k\) that originate or terminate at a given node. Formally, an edge-disjoint path is a simple path between two nodes that does not share any edge with another counted path. The number of edge-disjoint paths between two nodes is equivalent to the maximum flow between them [3]. Nodes with higher edge-disjoint \(k\)-path centrality are more robustly connected and, therefore, harder to isolate from 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.
[3] Ford, L.R., & Fulkerson, D.R. (1962). Flows in Networks. Princeton University Press, Princeton.