A mathematical analysis of the R-MAT random graph generator

The R-MAT graph generator introduced by Chakrabarti et al (Int Conf Data Mining, 2004) offers a simple, fast method for generating very large directed graphs. These properties have made it a popular choice as a method of generating graphs for objects of study in a variety of disciplines, from social network analysis to high performance computing. We analyze the graphs generated by R-MAT and model the generator in terms of occupancy problems to prove results about the degree distributions of these graphs. We prove that the limiting degree distributions can be expressed as a mixture of normal distributions with means and variances that can be easily calculated from the R-MAT parameters. Additionally, this article offers an efficient computational technique for computing the exact degree distribution and concise expressions for a number of properties of R-MAT graphs. ©2011 Wiley Periodicals, Inc.*. NETWORKS, 2011 The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes.