Emergent structures in large networks

TL;DR

This paper investigates phase transitions in large exponential random graph models, demonstrating the emergence of multipartite structures in certain parameter regions and identifying a transition from disordered graphs.

Contribution

It proves the existence of a phase transition leading to multipartite structures in exponential random graph models.

Findings

Existence of a parameter region with multipartite structure

Identification of a phase transition separating disordered and structured graphs

Theoretical characterization of emergent network structures

Abstract

We consider a large class of exponential random graph models and prove the existence of a region of parameter space corresponding to multipartite structure, separated by a phase transition from a region of disordered graphs.