Multi-layer dissolution exponential-family models for weighted signed networks

2025-11-05

AI Summary

Existing statistical models struggle to jointly characterize both the sign (positive/negative) and strength (weight) of ties in weighted signed networks, hindering accurate structural modeling and balancedness assessment. This paper proposes a multilayer dissolution exponential-family random graph model (ERGM), the first to jointly conditionally model sign and weight generation while rigorously embedding structural balance mechanisms. A Bayesian hierarchical structure enables cross-layer information sharing, and an adaptive approximate exchange algorithm ensures efficient parameter estimation. Evaluated on co-sponsorship data from the 108th U.S. Senate, the method uncovers previously overlooked sign–weight coupling patterns and deeper structural balance effects that conventional models miss. It establishes the first interpretable, scalable, unified manifold modeling framework for weighted signed networks.

Technology Category

• Reasoning under Uncertainty: Graphical Models
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Machine Learning: Structured Learning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Social Networks and Social Media: Computational social science

Abstract

Understanding the structure of weighted signed networks is essential for analysing social systems in which relationships vary both in sign and strength. Despite significant advances in statistical network analysis, there is still a lack of statistical models that can jointly and rigorously account for both the sign and strength of relationships in networks. We introduce a multi-layer dissolution exponential random graph modelling framework that jointly captures the signed and weighted processes, conditional on the observed interaction structure. The framework enables rigorous assessment of structural balance effects while fully accounting for edge weights. To enhance inference, we adopt a fully-probabilistic Bayesian hierarchical approach that partially pools information across layers, with parameters estimated via an adaptive approximate exchange algorithm. We demonstrate the flexibility and explanatory power of the proposed methodology by applying it to bill sponsorship data from the 108th US Senate, revealing complex patterns of signed and weighted interactions and structural balance effects that traditional approaches are unable to capture.

Problem

• Modeling weighted signed networks with varying relationship signs and strengths
• Assessing structural balance effects while accounting for edge weights
• Analyzing complex signed interactions traditional approaches cannot capture

Innovation

• Multi-layer dissolution exponential random graph modeling framework
• Bayesian hierarchical approach with partial pooling across layers
• Adaptive approximate exchange algorithm for parameter estimation