Practical methods for graph two-sample testing

TL;DR

This paper evaluates existing graph two-sample tests, highlights their limitations, and introduces two new, computationally efficient tests based on asymptotic distributions that improve reliability in large graph analysis.

Contribution

It proposes two novel tests for graph two-sample testing that are more practical and reliable than existing methods, especially for large graphs.

Findings

Existing tests have practical limitations.

Proposed tests are computationally less expensive.

New tests show improved reliability in certain scenarios.

Abstract

Hypothesis testing for graphs has been an important tool in applied research fields for more than two decades, and still remains a challenging problem as one often needs to draw inference from few replicates of large graphs. Recent studies in statistics and learning theory have provided some theoretical insights about such high-dimensional graph testing problems, but the practicality of the developed theoretical methods remains an open question. In this paper, we consider the problem of two-sample testing of large graphs. We demonstrate the practical merits and limitations of existing theoretical tests and their bootstrapped variants. We also propose two new tests based on asymptotic distributions. We show that these tests are computationally less expensive and, in some cases, more reliable than the existing methods.