Singularities in the entropy of asymptotically large simple graphs

TL;DR

This paper investigates the entropy behavior of large simple graphs with fixed edge and triangle densities, revealing that the entropy function exhibits nondifferentiability along a specific curve, indicating phase transition-like phenomena.

Contribution

It establishes the nondifferentiability of the asymptotic entropy function of large graphs along a particular curve, highlighting a new structural property.

Findings

Entropy is nondifferentiable along a certain curve

Identifies a phase transition in graph entropy

Provides mathematical proof of the nondifferentiability

Abstract

We prove that the asymptotic entropy of large simple graphs, as a function of fixed edge and triangle densities, is nondifferentiable along a certain curve.