A detailed investigation into near degenerate exponential random graphs

Abstract

The exponential family of random graphs has been a topic of continued research interest. Despite the relative simplicity, these models capture a variety of interesting features displayed by large-scale networks and allow us to better understand how phases transition between one another as tuning parameters vary. As the parameters cross certain lines, the model asymptotically transitions from a very sparse graph to a very dense graph, completely skipping all intermediate structures. We delve deeper into this near degenerate tendency and give an explicit characterization of the asymptotic graph structure as a function of the parameters.

15 pages, 3 figures, 2 tables

References in corpus (3)

• Solution for the properties of a clustered network
• On the phase transition curve in a directed exponential random graph model
• Asymptotics for Sparse Exponential Random Graph Models

Cited by in corpus (4)

• Imaginary replica analysis of loopy regular random graphs
• Exactly Solvable Random Graph Ensemble with Extensively Many Short Cycles
• Phase Transitions in Edge-Weighted Exponential Random Graphs: Near-Degeneracy and Universality
• Free-energy density functional for Strauss's model of transitive networks