Bipartite Graphs as Models of Complex Networks

TL;DR

This paper introduces a bipartite graph model for complex networks that captures key properties like clustering, degree distribution, and average distance, based on real-world observations and simple to analyze.

Contribution

It presents a bipartite graph model that accurately reflects complex network properties and a growing model based on this bipartite structure.

Findings

The model reproduces clustering, degree distribution, and average distance.

Any complex network can be viewed as a bipartite graph with specific features.

A growing bipartite model is proposed to simulate network evolution.

Abstract

It appeared recently that the classical random graph model used to represent real-world complex networks does not capture their main properties. Since then, various attempts have been made to provide accurate models. We study here a model which achieves the following challenges: it produces graphs which have the three main wanted properties (clustering, degree distribution, average distance), it is based on some real-world observations, and it is sufficiently simple to make it possible to prove its main properties. This model consists in sampling a random bipartite graph with prescribed degree distribution. Indeed, we show that any complex network may be viewed as a bipartite graph with some specific characteristics, and that its main properties may be viewed as consequences of this underlying structure. We also propose a growing model based on this observation.