Statistical hypothesis testing for differences between layers in dynamic multiplex graphs
File(s)
Accepted version
Author(s)
Baum, Maximilian
Sanna Passino, Francesco
Gandy, Axel
Type
Journal Article
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.
Date Issued
2026-09-08
Date Acceptance
2026-09-08
Citation
IEEE Transactions on Signal and Information Processing over Networks
ISSN
2373-7778
Publisher
Institute of Electrical and Electronics Engineers
Journal / Book Title
IEEE Transactions on Signal and Information Processing over Networks
Copyright Statement
Copyright This paper is embargoed until publication. Once published the author’s accepted manuscript will be made available under a CC-BY License in accordance with Imperial’s Research Publications Open Access policy (www.imperial.ac.uk/oa-policy).
License URL
Identifier
https://arxiv.org/abs/2512.03983v3
Subjects
stat.ME
stat.ME
Publication Status
Accepted
Date Publish Online
2026-09-20