Exponential-Family Random Graph Models for Multi-Layer Networks.

Area of Science:

• Network Science
• Statistical Modeling
• Sociology

Background:

• Multi-layer networks involve multiple relationship types among common actors.
• Existing exponential-family random graph models (ERGMs) are limited in analyzing dependencies across more than two layers.
• There is a need for flexible ERGM frameworks to capture complex relational structures.

Purpose of the Study:

• To extend the exponential-family random graph model (ERGM) framework for analyzing multi-layer networks with more than two layers.
• To introduce novel statistical distributions and modeling components for multi-layer ERGMs.
• To demonstrate the applicability of the developed methods on real-world network data.

Main Methods:

• Development of a Conway-Maxwell-Binomial distribution to model marginal dependence across multiple network layers.
• Introduction of a "layer logic" language for translating standard ERGM effects to multi-layer interactions.
• Inclusion of nondegenerate triadic and degree effects suitable for multi-layer network analysis.

Main Results:

• The proposed extensions successfully model marginal dependence among multiple network layers.
• The "layer logic" provides a flexible way to specify complex interactions in multi-layer networks.
• The developed methods were effectively demonstrated on two empirical datasets, showing improved modeling capabilities.

Conclusions:

• The extended ERGM framework offers a powerful new approach for analyzing complex multi-layer network structures.
• These advancements overcome limitations of previous ERGM applications, enabling richer insights into systems with multiple relational layers.
• The methods provide a valuable tool for researchers studying interconnected systems in various scientific domains.