Two-Sample Tests for Large Random Graphs Using Network Statistics
This provides a method for comparing networks like Facebook and LinkedIn, addressing a domain-specific need in network analysis.
The paper tackles the problem of two-sample hypothesis testing for large random graphs using network statistics, presenting a consistent and minimax optimal test without assumptions about the network generation process.
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.