Betweenness Central Nodes Under Uncertainty: An Absorbing Markov Chain Approach

2026-05-14

AI Summary

This study addresses the challenge of reliably identifying critical nodes in uncertain networks characterized by random edge failures and stochastic weight variations, where traditional betweenness centrality proves unstable. The authors propose a novel framework that, for the first time, formulates the problem using absorbing Markov chains, quantifying node importance via the proportion of time spent at each transient state before absorption. An efficient Monte Carlo simulation scheme is employed to estimate these occupancy measures. The approach naturally accommodates weighted reward mechanisms and candidate-set constraints, while robustness of rankings is analyzed through perturbation of the transition kernel. Experiments demonstrate that the method effectively identifies a small set of dominant nodes across diverse random graph models—including Erdős–Rényi and Watts–Strogatz networks—distinguishes between stable and sensitive rankings, and flexibly adapts to structural and reward-based variations.

Abstract

We propose a betweenness centrality measure and algorithms for stochastic networks, where edges can fail and weights vary across realizations, making the most central node random. Our approach models the sequence of reported central nodes as an absorbing Markov chain and measures node importance by the share of pre-absorption time spent at each node. This produces a way to study centrality under uncertainty, which can then be estimated with Monte Carlo simulation. We also analyze robustness when the transition kernel is only approximately known, using row-wise perturbations to assess sensitivity and potential ranking changes. The framework further admits extensions to weighted rewards and restricted candidate sets without altering the Markov chain formulation. Experiments on Erdős-Rényi, Watts-Strogatz, and Les Misérables networks with stochastic edges show that the method identifies a small set of dominant nodes, reveals stable versus sensitive rankings under perturbations, and supports reward-based and structure-constrained variants.

Problem

• betweenness centrality
• stochastic networks
• network uncertainty
• central nodes
• edge failure

Innovation

• betweenness centrality
• absorbing Markov chain
• stochastic networks
• Monte Carlo simulation
• robustness analysis