EDGE EXCHANGEABLE MODELS FOR INTERACTION NETWORKS.

Area of Science:

• Network Science
• Statistical Modeling
• Data Analysis

Background:

• Modern network datasets often originate from population interactions (e.g., calls, collaborations).
• Edges, not vertices, are the fundamental units in many interaction networks.
• Existing vertex-centric models struggle with sparse structures and power-law degree distributions.

Purpose of the Study:

• To introduce and study edge exchangeable network models for statistical analysis.
• To provide a framework better suited for interaction network properties.
• To develop models that naturally handle sparsity and power-law distributions.

Main Methods:

• Initiating the study of edge exchangeable network models.
• Exploring fundamental statistical properties of these models.
• Identifying the Hollywood model as a canonical edge exchangeable distribution family.

Main Results:

• Edge exchangeable models offer theoretical and practical advantages over vertex-centric approaches.
• These models naturally accommodate sparse network structures and power-law degree distributions.
• The Hollywood model demonstrates computational tractability, interpretability, and good performance.

Conclusions:

• Edge exchangeable network models provide a more appropriate statistical framework for interaction networks.
• The Hollywood model is a practical and theoretically sound choice for network analysis.
• The vertex components model offers a nonparametric generalization with a stick-breaking construction.