Pairwise disconnectivity centrality quantifies the topological importance of a node by comparing the number of ordered node pairs that are reachable before and after its removal [2]. A node is more central if its removal disconnects a larger fraction of node pairs. Formally, the centrality of node \(i\) is defined as
\begin{equation*}
c_{\mathrm{pd}}(i) = \frac{n_G - n_{G_i}}{n_G},
\end{equation*}
where \(n_G\) is the total number of ordered pairs of nodes connected by at least one directed path in the graph \(G\), and \(G_i\) denotes the graph obtained by removing 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] Potapov, A. P., Goemann, B., & Wingender, E. (2008). The pairwise disconnectivity index as a new metric for the topological analysis of regulatory networks. BMC bioinformatics, 9(1), 227. doi: 10.1186/1471-2105-9-227.