# Ground States for Exponential Random Graphs

## TL;DR

This paper introduces a perturbative approach to estimate normalization constants in exponential random graph models and provides evidence of phase transition phenomena in the edge-triangle model.

## Contribution

It presents a novel perturbative method for normalization estimation and demonstrates discontinuity in model behavior at critical parameter values.

## Key findings

- Perturbative method effectively estimates normalization constants.
- Evidence of phase transition in the edge-triangle model.
- Discontinuity observed along critical directions.

## Abstract

We propose a perturbative method to estimate the normalization constant in exponential random graph models as the weighting parameters approach infinity. As an application, we give evidence of discontinuity in natural parametrization along the critical directions of the edge-triangle model.