Scalable signed exponential random graph models under local dependence

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, a novel method that combines the strengths of SBM and ERGM while mitigating their weaknesses by incorporating local dependence based on nonoverlapping blocks is proposed. The approach involves a two-step process: First, decomposing the network into sub-networks using SBM approximation, and, second, estimating parameters using ERGM methods. The method is validated on large synthetic networks and applied to a signed Wikipedia network of thousands of editors. Through the use of local dependence, patterns consistent with structural balance theory are found.