Title: Higher-order accurate two-sample network inference and network hashing

Abstract: Two-sample hypothesis testing for network comparison presents many significant challenges, including: leveraging repeated network observations and known node registration, but without requiring them to operate; relaxing strong structural assumptions; achieving finite-sample higher-order accuracy; handling different network sizes and sparsity levels; fast computation and memory parsimony; controlling false discovery rate (FDR) in multiple testing; and theoretical understandings, particularly regarding finite-sample accuracy and minimax optimality.  In this paper, we develop a comprehensive toolbox, featuring a novel main method and its variants, all accompanied by strong theoretical guarantees, to address these challenges.  Our method outperforms existing tools in speed and accuracy, and it is proved power-optimal.  Our algorithms are user-friendly and versatile in handling various data structures (single or repeated network observations; known or unknown node registration).  We also develop an innovative framework for offline hashing and fast querying as a very useful tool for large network databases.  We showcase the effectiveness of our method through comprehensive simulations and applications to two real-world datasets, which revealed intriguing new structures.