A Practical Two-Sample Test for Weighted Random Graphs

TL;DR

This paper introduces a practical statistical test for comparing two weighted graph populations, addressing a gap in existing methods that are limited to binary graphs, and demonstrates its effectiveness through theory, simulations, and real data.

Contribution

The paper proposes a new test statistic for weighted graph two-sample testing, with proven distributional convergence and improved performance over existing binary graph methods.

Findings

Test statistic converges to standard normal under null hypothesis

Proposed test outperforms existing binary graph tests in simulations

Method is validated with real-world data application

Abstract

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.