Betweenness Central Nodes Under Uncertainty: An Absorbing Markov Chain Approach
For network analysts dealing with uncertain or dynamic networks, this provides a principled way to quantify node importance when centrality is random.
The paper proposes a betweenness centrality measure for stochastic networks where edges can fail or weights vary, modeling central node sequences as an absorbing Markov chain. Experiments on synthetic and real networks show the method identifies dominant nodes and reveals ranking stability under perturbations.
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.