Two-Sample Tests for Large Random Graphs Using Network Statistics

TL;DR

This paper develops a general, assumption-free method for two-sample hypothesis testing on large undirected graphs, using network statistics, with proven optimality for certain cases.

Contribution

It introduces a new, general framework for two-sample tests on large graphs based on concentration of network statistics, without assuming specific network models.

Findings

Proposes a consistent two-sample test based on network statistics.

Shows the test is minimax optimal for certain statistics.

Applicable to real-world networks like Facebook and LinkedIn.

Abstract

We consider a two-sample hypothesis testing problem, where the distributions are defined on the space of undirected graphs, and one has access to only one observation from each model. A motivating example for this problem is comparing the friendship networks on Facebook and LinkedIn. The practical approach to such problems is to compare the networks based on certain network statistics. In this paper, we present a general principle for two-sample hypothesis testing in such scenarios without making any assumption about the network generation process. The main contribution of the paper is a general formulation of the problem based on concentration of network statistics, and consequently, a consistent two-sample test that arises as the natural solution for this problem. We also show that the proposed test is minimax optimal for certain network statistics.