A simple method for improving the accuracy of Chung-Lu random graph generation

TL;DR

This paper presents a straightforward method to enhance the accuracy of Chung-Lu random graph generation by using a Poisson approximation and a linear system inversion, significantly reducing degree sequence errors.

Contribution

It introduces a novel, simple approach employing a Poisson approximation and linear system inversion to improve Chung-Lu graph generation accuracy.

Findings

Reduces degree sequence error in Chung-Lu graph generation

Provides a closed-form expression for the inverse linear system

Significantly improves accuracy across various degree distributions

Abstract

Random graph models play a central role in network analysis. The Chung-Lu model, which connects nodes based on their expected degrees is of particular interest. It is widely used to generate null-graph models with expected degree sequences as well as implicitly define network measures such as modularity. Despite its popularity, practical methods for generating instances of Chung-Lu model-based graphs do relatively poor jobs in terms of accurately realizing many degree sequences. We introduce a simple method for improving the accuracy of Chung-Lu graph generation. Our method uses a Poisson approximation to define a linear system describing the expected degree sequence to be output from the model using standard generation techniques. We then use the inverse of this system to determine an appropriate input corresponding to the desired output. We give a closed form expression for this inverse and show that it may be used to drastically reduce error for many degree distributions.