Exchangeable Random Networks

TL;DR

This paper introduces exchangeable random graph ensembles as versatile models for empirical and theoretical network analysis, providing characterizations of degree distributions, subgraph features, and applications to directed networks with power-law degrees.

Contribution

It presents a new class of exchangeable random networks with comprehensive theoretical properties and demonstrates their flexibility through detailed analysis of directed power-law networks.

Findings

Characterization of degree distributions in exchangeable graphs

Analysis of subgraph and adjacency matrix features

Application to directed networks with power-law out-degree

Abstract

We introduce and study a class of exchangeable random graph ensembles. They can be used as statistical null models for empirical networks, and as a tool for theoretical investigations. We provide general theorems that carachterize the degree distribution of the ensemble graphs, together with some features that are important for applications, such as subgraph distributions and kernel of the adjacency matrix. These results are used to compare to other models of simple and complex networks. A particular case of directed networks with power-law out--degree is studied in more detail, as an example of the flexibility of the model in applications.