Inference for Balance in Dynamic Signed Networks

2026-06-07

AI Summary

This study addresses the challenge of inferring structural balance in dynamic signed networks at arbitrary time points, particularly when direct observations are unavailable or data are sparse. The authors propose a nonparametric approach based on a dynamic signed graph model, which employs kernel smoothing to aggregate information from neighboring time snapshots and estimate the balance level at the target time. A studentized test statistic is constructed for hypothesis testing, enabling, for the first time, nonparametric inference of structural balance in continuous time. By incorporating an Edgeworth expansion, the method provides a higher-order approximation of the test statistic’s distribution and reveals how temporal smoothing enhances signal recovery and suppresses noise in sparse regimes. Theoretical guarantees establish the method’s validity, simulations confirm its finite-sample performance, and an application to international relations networks demonstrates its practical utility.

Abstract

Signed networks consist of both positive and negative relations, and structural balance theory provides an important conceptural framework for understanding their global tension structure. While existing statistical methods mainly focus on assessing empirical evidence of balance in a single observed network, many real-world signed relations evolve over time. This paper develops nonparametric inference for the population degree of structural balance at specified time points in dynamic signed networks, where the target time may or may not coincide with an observed snapshot. We consider a dynamic signed graphon model in which both edge formation and sign generation are governed by smoothly time-varying graphon functions. To exploit temporal smoothness, we construct a kernel-smoothed estimator that borrows information from snapshots near the target time point. Our theoretical analysis establishes a studentized inference procedure and a higher-order distributional approximation based on Edgeworth expansion, showing that temporal smoothing improves inference in sparse networks by reducing variance of observation noise, up to smoothing bias and time-discretization errors. We demonstrate the finite-sample performance and practical usefulness of the proposed method through extensive simulation studies and an application to a dynamic international relation network in political science.

Problem

• dynamic signed networks
• structural balance
• nonparametric inference
• temporal smoothing
• graphon model

Innovation

• dynamic signed networks
• structural balance
• graphon model
• kernel smoothing
• nonparametric inference