Scalable Signed Exponential Random Graph Models under Local Dependence

TL;DR

This paper introduces a scalable method for analyzing large signed networks by combining SBM and ERGM with local dependence, enabling effective modeling of complex social interactions.

Contribution

It proposes a novel two-step approach that decomposes networks into blocks and estimates parameters, addressing limitations of traditional models in large, signed networks.

Findings

Patterns consistent with structural balance theory were identified.

The method performs well on large synthetic networks.

Applied successfully to a signed Wikipedia editor network.

Abstract

Traditional network analysis focuses on binary edges, while real-world relationships are more nuanced, encompassing cooperation, neutrality, and conflict. The rise of negative edges in social media discussions spurred interest in analyzing signed interactions, especially in polarized debates. However, the vast data generated by digital networks presents challenges for traditional methods like Stochastic Block Models (SBM) and Exponential Family Random Graph Models (ERGM), particularly due to the homogeneity assumption and global dependence, which become increasingly unrealistic as network size grows. To address this, we propose a novel method that combines the strengths of SBM and ERGM while mitigating their weaknesses by incorporating local dependence based on nonoverlapping blocks. Our approach involves a two-step process: First, decomposing the network into sub-networks using SBM approximation, and, second, estimating parameters using ERGM methods. We validate our method on large synthetic networks and apply it to a signed Wikipedia network of thousands of editors. Through the use of local dependence, we find patterns consistent with structural balance theory.