Equitable random graphs

TL;DR

This paper introduces equitable random graphs, a versatile class of models capable of representing complex network structures while remaining exactly solvable for key properties in large networks.

Contribution

It presents a new class of random graph models that generalize existing models and are analytically tractable for diverse network features.

Findings

Can model networks with community, bipartite, and stratified structures

Exactly solvable for percolation, spectral density, and dynamical behaviors

Applicable to large-scale network analysis

Abstract

Random graph models have played a dominant role in the theoretical study of networked systems. The Poisson random graph of Erdos and Renyi, in particular, as well as the so-called configuration model, have served as the starting point for numerous calculations. In this paper we describe another large class of random graph models, which we call equitable random graphs and which are flexible enough to represent networks with diverse degree distributions and many nontrivial types of structure, including community structure, bipartite structure, degree correlations, stratification, and others, yet are exactly solvable for a wide range of properties in the limit of large graph size, including percolation properties, complete spectral density, and the behavior of homogeneous dynamical systems, such as coupled oscillators or epidemic models.