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arXiv · 2111.03005

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

Daniel Allendorf·Ulrich Meyer·Manuel Penschuck·Hung Tran
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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.

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Daniel Allendorf, Ulrich Meyer, Manuel Penschuck, Hung Tran. 2023-02-15. Parallel Global Edge Switching for the Uniform Sampling of Simple Graphs with Prescribed Degrees. https://doi.org/10.1016/j.jpdc.2022.12.010

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