A Bootstrap-based Method for Testing Similarity of Matched Networks

This article studies the matched network inference problem, where the goal is to determine if two networks, defined on a common set of nodes, exhibit a specific form of stochastic similarity. Two notions of similarity are considered: (i) equality, that is, testing whether the networks arise from the same random graph model, and (ii) scaling, that is, testing whether their probability matrices are proportional for some unknown scaling constant. We develop a testing framework based on a parametric bootstrap approach and a Frobenius norm-based test statistic. The proposed approach is highly versatile as it covers both the equality and scaling problems, and ensures adaptability under various model settings, including stochastic blockmodels, Chung-Lu models, and random dot product graph models. We establish theoretical consistency of the proposed tests and demonstrate their empirical performance through extensive simulations under a wide range of model classes. Our results establish the flexibility and computational efficiency of the proposed method compared to existing approaches. We also report a real-world application involving the Aarhus network dataset, which reveals meaningful sociological patterns across different communication layers. Supplementary materials for this article are available online.