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

TL;DR

This paper introduces a new statistical test based on e-values for detecting community structures in evolving temporal networks, addressing a gap in existing methods for dynamic network analysis.

Contribution

It proposes a novel e-value based testing framework specifically designed for temporal networks, which remains valid even with dependent data over time.

Findings

Effective in synthetic and real-world networks

Retains validity with dependent temporal data

Highlights challenges in testing temporal community structures

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.