On the Geometry and Extremal Properties of the Edge-Degeneracy Model

TL;DR

This paper investigates the geometric and extremal properties of the edge-degeneracy exponential random graph model, providing insights into its statistical behavior through polytope analysis.

Contribution

It introduces a geometric perspective on the edge-degeneracy model, analyzing its properties via the associated polytope to understand its statistical degeneracy.

Findings

The model is relatively well-behaved.

Polytope geometry reveals extremal properties.

Insights into the model's degeneracy behavior.

Abstract

The edge-degeneracy model is an exponential random graph model that uses the graph degeneracy, a measure of the graph's connection density, and number of edges in a graph as its sufficient statistics. We show this model is relatively well-behaved by studying the statistical degeneracy of this model through the geometry of the associated polytope.