A standard CLT for triangles in a class of ERGs

TL;DR

This paper establishes a Central Limit Theorem for the number of triangles in a specific class of exponential random graphs, using a polynomial approach to analyze the partition function across the entire analyticity region.

Contribution

It introduces a CLT for triangles in ERGs with a novel polynomial representation of the partition function, extending results to the full analyticity region.

Findings

CLT proven for normalized triangle counts in ERGs

Polynomial representation of the partition function is key

Results apply across the entire analyticity region

Abstract

We prove a standard Central Limit Theorem for the (normalized) number of triangles in a class of Exponential Random Graphs derived from a slight modification of the edge-triangle model. Our main theorem covers the whole analyticity region of the free energy, and is based on a polynomial representation of the partition function.