A practical two-sample test for weighted random graphs

• Published in: Journal of applied statistics Vol. 50; no. 3; pp. 495 - 511
• Main Authors: Yuan, Mingao, Wen, Qian
• Format: Journal Article
• Language: English
• Published: England Taylor & Francis 17-02-2023; Taylor & Francis Ltd
• Subjects: Data analysis; Graphs; Machine learning; Normal distribution; Null hypothesis; random graph; Statistical analysis; Statistical methods; Statistical tests; Two-sample hypothesis test; weighted graph; weighted graph; Two-sample hypothesis test; random graph
• ISSN: 0266-4763; 1360-0532
• DOI: 10.1080/02664763.2021.1884847

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 cannot 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.