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

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.

9 pages, 4 figures. This version differs ever so slightly from the published one; several typos have been fixed and clarifying comments by J. Rauh incorporated in the update

References in corpus (4)

• Identification of influential spreaders in complex networks
• New Model of Internet Topology Using k-shell Decomposition
• Maximum likelihood estimation in log-linear models
• Maximum lilkelihood estimation in the $\beta$-model

Cited by in corpus (1)

• Cores, shell indices and the degeneracy of a graph limit