A Spectral-Based Framework for Hypothesis Testing in Populations of Networks

In this paper, we propose a new spectral-based approach to hypothesis testing for populations of networks.The primary goal is to develop a test to determine whether two given samples of networks come from the same random model or distribution.Our test statistic is based on the trace of a centered and scaled adjacency matrix to the third power, which we prove converges to the standard normal distribution as the number of nodes tends to infinity.The asymptotic power guarantee of the test is also provided.The proper interplay between the number of networks and the number of nodes for each network is explored in characterizing the theoretical properties of the proposed testing statistic.Our test is applicable to both binary and weighted networks, operates under a very general framework where the networks are allowed to be large and sparse, and can be extended to multiple-sample testing.We provide an extensive simulation study to demonstrate the superior performance of our tests over the existing methods and apply our tests to three real datasets.