Phase transitions in exponential random graphs

TL;DR

This paper derives the complete phase diagram for a broad class of exponential random graph models, revealing phase transitions and critical points that enhance understanding of their structural properties.

Contribution

It provides the first full phase diagram for two-parameter exponential random graph models, including transition curves and critical points.

Findings

Identification of a first order transition curve

Existence of a critical point in the phase diagram

Comprehensive characterization of phase behavior

Abstract

We derive the full phase diagram for a large family of two-parameter exponential random graph models, each containing a first order transition curve ending in a critical point.