Parallel Global Edge Switching for the Uniform Sampling of Simple Graphs with Prescribed Degrees

TL;DR

This paper introduces a parallel version of the global edge switching Markov chain (G-ES-MC) for uniform sampling of graphs with prescribed degrees, demonstrating improved efficiency and scalability over traditional methods.

Contribution

It proposes the G-ES-MC, a new Markov chain with simpler dependencies, and develops shared-memory parallel algorithms for efficient graph sampling.

Findings

G-ES-MC converges to the uniform distribution.

Parallel G-ES-MC is more efficient and scalable.

G-ES-MC often requires fewer switches than ES-MC.

Abstract

The uniform sampling of simple graphs matching a prescribed degree sequence is an important tool in network science, e.g. to construct graph generators or null-models. Here, the Edge Switching Markov Chain (ES-MC) is a common choice. Given an arbitrary simple graph with the required degree sequence, ES-MC carries out a large number of small changes, called edge switches, to eventually obtain a uniform sample. In practice, reasonably short runs efficiently yield approximate uniform samples. In this work, we study the problem of executing edge switches in parallel. We discuss parallelizations of ES-MC, but find that this approach suffers from complex dependencies between edge switches. For this reason, we propose the Global Edge Switching Markov Chain (G-ES-MC), an ES-MC variant with simpler dependencies. We show that G-ES-MC converges to the uniform distribution and design shared-memory parallel algorithms for ES-MC and G-ES-MC. In an empirical evaluation, we provide evidence that G-ES-MC requires not more switches than ES-MC (and often fewer), and demonstrate the efficiency and scalability of our parallel G-ES-MC implementation.