Two‐sample testing for random graphs

The employment of two‐sample hypothesis testing in examining random graphs has been a prevalent approach in diverse fields such as social sciences, neuroscience, and genetics. We advance a spectral‐based two‐sample hypothesis testing methodology to test the latent position random graphs. We propose two distinct asymptotic normal statistics, each optimally designed for two different models—the elementary Erdős–Rényi model and the more complex latent position random graph model. For the latter, the spectral embedding of the adjacency matrix was utilized to estimate the test statistic. The proposed method exhibited superior efficacy as it accomplished higher power than the conventional method of mean estimation. To validate our hypothesis testing procedure, we applied it to empirical biological data to discern structural variances in gene co‐expression networks between COVID‐19 patients and individuals who remained unaffected by the disease.