Parallel Generation of Simple Null Graph Models

Jack Garbus, Christopher Brissette, George M. Slota

Abstract: The generation of uniformly-random graphs is a key analytic tool for hypothesis testing throughout social network analysis. This work specifically optimizes the generation of large-scale simple uniform random graphs. We consider the separate but related problems of generating such a graph from an existing edge list and the problem of generating a graph from only a degree distribution. To address these problems, we implement an efficient parallel Markov Chain Monte Carlo process for double-edge swapping, a fast and parallel method for edge-skipping edge list generation, and a novel method to solve for valid inputs to our edge-skipping generator. Our double-edge swapping procedure is considerably faster than prior parallel methods, our edge generator uses state-of-the-art methods, and the algorithmic approach we have to solve for valid edge-skipping inputs addresses the often significant shortcomings of current approaches.