Statistical hypothesis testing for differences between layers in dynamic multiplex networks

TL;DR

This paper introduces a spectral embedding-based hypothesis testing framework for detecting differences between layers in dynamic multiplex networks, applicable to large graphs and adaptable to temporal comparisons.

Contribution

It extends existing methods to enable global testing of layer differences in multiplex networks under a latent space model, with demonstrated effectiveness on simulated and biological data.

Findings

The test accurately detects layer differences asymptotically.

Finite-sample tests perform well on simulated data.

Application to neural activity data shows practical utility.

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.