A generalized hypothesis test for community structure in networks

TL;DR

This paper introduces a statistically rigorous, model-agnostic hypothesis testing framework to determine whether a network exhibits meaningful community structure, providing theoretical validation and practical insights.

Contribution

It develops a new hypothesis test based on a general community structure parameter, applicable across different models, with proven properties and real-world data applications.

Findings

The tests effectively identify community structure in various networks.

The method provides interpretable results and theoretical guarantees.

Applications reveal meaningful community patterns in real data.

Abstract

Researchers theorize that many real-world networks exhibit community structure where within-community edges are more likely than between-community edges. While numerous methods exist to cluster nodes into different communities, less work has addressed this question: given some network, does it exhibit statistically meaningful community structure? We answer this question in a principled manner by framing it as a statistical hypothesis test in terms of a general and model-agnostic community structure parameter. Leveraging this parameter, we propose a simple and interpretable test statistic used to formulate two separate hypothesis testing frameworks. The first is an asymptotic test against a baseline value of the parameter while the second tests against a baseline model using bootstrap-based thresholds. We prove theoretical properties of these tests and demonstrate how the proposed method yields rich insights into real-world data sets.