Random Graphs from Random Matrices

TL;DR

This paper introduces a novel class of random graph models derived from symmetric matrices using the order complex, revealing unexpected phase transition phenomena through experimental analysis.

Contribution

It proposes a new approach to generate random graphs from matrices via order complexes and demonstrates surprising phase transition behaviors.

Findings

Identification of sharp phase transitions in the new graph models

Experimental evidence of unexpected behaviors in graph properties

Introduction of a matrix-based framework for random graph generation

Abstract

We use the order complex corresponding to a symmetric matrix (defined by Giusti et al in 2015). In this note, we use it to define a class of models of random graphs, and show some surprising experimental results, showing sharp phase transitions.