[edit]

# Two-Sample Tests for Large Random Graphs Using Network Statistics

*Proceedings of the 2017 Conference on Learning Theory*, PMLR 65:954-977, 2017.

#### 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.