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arXiv · 2605.14743

Computing Absorbing-Frequency Centrality: Complexity, Estimators, and Scalable Algorithms for Stochastic Networks

Wencheng Bao·Eleftheria Kontou·Chrysafis Vogiatzis
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Abstract

In a stochastic network, where edges fail and weights may vary across realizations, the node of highest betweenness is itself random. Absorbing-frequency centrality (AFC) scores each node by how often it is reported as the node of highest betweenness: the reported betweenness maximizer traces an absorbing Markov chain, and AFC is the normalized expected pre-absorption occupancy. Computing it exactly is intractable: we prove that evaluating even a single transition probability of the AFC chain is #P-hard, by a reduction from two-terminal network reliability, and that the expected absorption time and AFC scores inherit this hardness. We develop a matrix estimator that builds the kernel row-wise and solves one linear system, and a parallelizable episode estimator over absorption trajectories that is strongly consistent and asymptotically normal, with finite-sample guarantees tied to the empirical error decay. A computational study reports scalability on Erd\H{o}s-R\'enyi, Watts-Strogatz, and Barab\'asi-Albert graphs, and a monitor placement experiment in which AFC's advantage over pooled counting generally grows with reliability heterogeneity.

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Wencheng Bao, Eleftheria Kontou, Chrysafis Vogiatzis. 2026-05-14. Computing Absorbing-Frequency Centrality: Complexity, Estimators, and Scalable Algorithms for Stochastic Networks. https://arxiv.org/abs/2605.14743

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