Stress centrality

Stress centrality quantifies the amount of "stress" a node experiences due to the network's activity, quantified by how often the node lies on the shortest paths connecting pairs of other nodes [2]. For a node \(i\), the stress centrality, denoted by \(c_{Stress}(i)\), is defined as the total number of shortest paths between all pairs of nodes that pass through \(i\):
\begin{equation*}
c_{Stress}(i) = \sum_{j \neq k \neq i} σ_{jk}(i),
\end{equation*}
where \(σ_{jk}(i)\) denotes the number of shortest paths from node \(j\) to node \(k\) that pass through node \(i\).

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] Shimbel, A. (1953). Structural parameters of communication networks. The bulletin of mathematical biophysics, 15(4), 501-507. doi: 10.1007/BF02476438.