  Network (graph) data analysis is a popular research topic in statistics and
machine learning. In application, one is frequently confronted with graph
two-sample hypothesis testing where the goal is to test the difference between
two graph populations. Several statistical tests have been devised for this
purpose in the context of binary graphs. However, many of the practical
networks are weighted and existing procedures can't be directly applied to
weighted graphs. In this paper, we study the weighted graph two-sample
hypothesis testing problem and propose a practical test statistic. We prove
that the proposed test statistic converges in distribution to the standard
normal distribution under the null hypothesis and analyze its power
theoretically. The simulation study shows that the proposed test has
satisfactory performance and it substantially outperforms the existing
counterpart in the binary graph case. A real data application is provided to
illustrate the method.
