On the uniform generation of random graphs with prescribed degree sequences

TL;DR

This paper reviews existing methods for generating random graphs with fixed degree sequences, introduces a new Monte Carlo approach, and evaluates their accuracy and efficiency for network analysis.

Contribution

It presents a novel 'go with the winners' Monte Carlo method and compares it to existing algorithms, highlighting its advantages and limitations.

Findings

The 'go with the winners' method is accurate but slow.

The switching method is fast and reliable for most practical purposes.

Existing methods have small deviations under realistic conditions.

Abstract

Random graphs with prescribed degree sequences have been widely used as a model of complex networks. Comparing an observed network to an ensemble of such graphs allows one to detect deviations from randomness in network properties. Here we briefly review two existing methods for the generation of random graphs with arbitrary degree sequences, which we call the ``switching'' and ``matching'' methods, and present a new method based on the ``go with the winners'' Monte Carlo method. The matching method may suffer from nonuniform sampling, while the switching method has no general theoretical bound on its mixing time. The ``go with the winners'' method has neither of these drawbacks, but is slow. It can however be used to evaluate the reliability of the other two methods and, by doing this, we demonstrate that the deviations of the switching and matching algorithms under realistic conditions are small compared to the ``go with the winners'' algorithm. Because of its combination of speed and accuracy we recommend the use of the switching method for most calculations.