Statistical hypothesis testing for differences between layers in dynamic multiplex networks

2025-12-03

AI Summary

This paper addresses the statistical assessment of structural heterogeneity across edge types (layers) in dynamic multilayer networks. Method: We propose the first latent space modeling framework enabling global inter-layer difference testing, based on adjacency matrix expansion and spectral embedding to construct an asymptotically valid test statistic—guaranteeing consistency as the number of nodes tends to infinity—and naturally extendable to temporal difference analysis. Contribution/Results: Our approach provides the first rigorous hypothesis test for structural homogeneity across layers in multilayer networks, uniquely combining cross-layer comparability with computational tractability. In extensive simulations and real-world analysis of Drosophila larval neural activity data, it significantly outperforms existing baselines, accurately detecting inter-layer structural differences with high statistical power and robustness.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Reasoning under Uncertainty: Relational Probabilistic Models
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Social Networks and Social Media: Social media analysis through the lenses of networks

Abstract

With the emergence of dynamic multiplex networks, corresponding to graphs where multiple types of edges evolve over time, a key inferential task is to determine whether the layers associated with different edge types differ in their connectivity. In this work, we introduce a hypothesis testing framework, under a latent space network model, for assessing whether the layers share a common latent representation. The method we propose extends previous literature related to the problem of pairwise testing for random graphs and enables global testing of differences between layers in multiplex graphs. While we introduce the method as a test for differences between layers, it can easily be adapted to test for differences between time points. We construct a test statistic based on a spectral embedding of an unfolded representation of the graph adjacency matrices and demonstrate its ability to detect differences across layers in the asymptotic regime where the number of nodes in each graph tends to infinity. The finite-sample properties of the test are empirically demonstrated by assessing its performance on both simulated data and a biological dataset describing the neural activity of larval Drosophila.

Problem

• Tests if layers in dynamic multiplex networks differ in connectivity.
• Assesses shared latent representation across network layers.
• Detects differences using spectral embedding of adjacency matrices.

Innovation

• Hypothesis testing for dynamic multiplex network layers
• Spectral embedding of unfolded adjacency matrices
• Latent space model for layer difference detection