Growing interest in modeling large, complexnetworks has spurred significant research into generative graphmodels. Kronecker-style models (e.g. SKG and R-MAT) are oftenused due to their scalability and ability to mimic key propertiesof real-world networks. Although a few papers theoreticallyestablish these models' behavior for specific parameters, manyclaims used to justify their use are supported only empirically. In this work, we prove several results using asymptotic analysiswhich illustrate that empirical studies may not fully capture thetrue behavior of the models. Paramount to the widespread adoption of Kronecker-stylemodels was the introduction of a linear-time edge-samplingvariant (R-MAT), which existing literature typically treats asinterchangeable with SKG. We prove that although several R-MAT formulations are asymptotically equivalent, their behaviordiverges from that of SKG. Further, we show these resultsare observable even at relatively small graph sizes. Second, weconsider a case where asymptotic analysis reveals unexpectedbehavior within a given model.
['Alex J. Chin', 'Timothy D. Goodrich', "Michael P. O'Brien", 'Felix Reidl', 'Blair D. Sullivan', 'Andrew van der Poel']
Asymptotic Analysis of Equivalences and Core-Structures in Kronecker-Style Graph Models