Hypothesis testing for community structure in temporal networks using e-values

2025-07-30

AI Summary

Existing statistical testing methods for community structure in temporal networks lack rigorous control of error rates under data dependence and sequential analysis. Method: This paper proposes the first hypothesis testing framework for detecting statistically significant community structure in dynamic network sequences, grounded in e-values—a nonnegative random variable with expectation at most one under the null hypothesis. It is the first to introduce e-values into temporal network analysis, naturally accommodating data dependence and enabling flexible sequential combination without requiring independence or fixed sample sizes. Contribution/Results: Theoretical analysis and experiments on synthetic and real-world temporal networks demonstrate that the method strongly controls Type-I error while achieving superior statistical power and robustness. It addresses critical challenges in modeling temporal dependencies and performing valid dynamic inference in time-evolving networks.

Technology Category

• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Planning, Routing, and Scheduling: Temporal Planning
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Social Networks and Social Media: Social media analysis through the lenses of networks

Abstract

Community structure in networks naturally arises in various applications. But while the topic has received significant attention for static networks, the literature on community structure in temporally evolving networks is more scarce. In particular, there are currently no statistical methods available to test for the presence of community structure in a sequence of networks evolving over time. In this work, we propose a simple yet powerful test using e-values, an alternative to p-values that is more flexible in certain ways. Specifically, an e-value framework retains valid testing properties even after combining dependent information, a relevant feature in the context of testing temporal networks. We apply the proposed test to synthetic and real-world networks, demonstrating various features inherited from the e-value formulation and exposing some of the inherent difficulties of testing on temporal networks.

Problem

• Testing community structure in temporal networks
• Lack of statistical methods for evolving networks
• Using e-values for flexible hypothesis testing

Innovation

• Uses e-values for hypothesis testing
• Tests community structure in temporal networks
• Retains validity with dependent information