Defining statistical ensembles of random graphs

TL;DR

This paper discusses how to define statistical ensembles of random graphs with arbitrary connectivity distributions, aiding the understanding of graph geometries beyond specific models, especially in the context of scale-free networks.

Contribution

It introduces a method to construct statistical ensembles of random graphs with any degree distribution, advancing the study of graph geometries independently of particular models.

Findings

Enables analysis of graph geometries across diverse degree distributions

Provides a framework for understanding scale-free network structures

Facilitates comparison of different random graph models

Abstract

The problem of defining a statistical ensemble of random graphs with an arbitrary connectivity distribution is discussed. Introducing such an ensemble is a step towards uderstanding the geometry of wide classes of graphs independently of any specific model. This research was triggered by the recent interest in the so-called scale-free networks.