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.

翻译：随着动态多层网络（即多种类型边随时间演化的图）的出现，一个关键的推断任务是判断不同边类型对应的层级在连接性上是否存在差异。本文在潜空间网络模型框架下，提出了一种假设检验方法，用于评估各层级是否共享共同的潜表征。该方法扩展了先前关于随机图两两比较问题的文献，能够实现对多层图中层级间差异的全局检验。虽然该方法最初被设计用于检验层级间差异，但可轻松调整为检验不同时间点间的差异。我们基于图邻接矩阵展开表示的谱嵌入构造检验统计量，并在每个图节点数趋于无穷的渐近框架下证明其检测层级间差异的能力。通过模拟数据及描述幼年果蝇神经活动的生物数据集，我们验证了该检验方法在有限样本下的性能表现。