Network Global Testing by Counting Graphlets

TL;DR

This paper introduces a new statistical testing framework for community detection in large, complex social networks by leveraging graphlet counts to effectively account for degree heterogeneity.

Contribution

It proposes a novel class of test statistics based on short path and cycle counts that cancel out degree effects, improving community detection accuracy.

Findings

Tests outperform existing methods in simulations

Framework effectively handles degree heterogeneity

Validated on real social network data

Abstract

Consider a large social network with possibly severe degree heterogeneity and mixed-memberships. We are interested in testing whether the network has only one community or there are more than one communities. The problem is known to be non-trivial, partially due to the presence of severe degree heterogeneity. We construct a class of test statistics using the numbers of short paths and short cycles, and the key to our approach is a general framework for canceling the effects of degree heterogeneity. The tests compare favorably with existing methods. We support our methods with careful analysis and numerical study with simulated data and a real data example.