A Bootstrap-based Method for Testing Network Similarity

TL;DR

This paper introduces a bootstrap-based statistical testing method to assess whether two networks are similar in structure, either exactly or proportionally, across various complex network models, with theoretical guarantees and practical applications.

Contribution

It develops a versatile bootstrap-based testing framework for network similarity that works across multiple models and provides theoretical and empirical validation.

Findings

The method accurately tests network equality and scaling.

It performs well across different network models.

Application to real data reveals sociological insights.

Abstract

This paper 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, i.e., testing whether the networks arise from the same random graph model, and (ii) scaling, i.e., 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.