Uniform Generation of Graphical Realizations of Joint Degree Matrices

Abstract

In this thesis, we introduce JDM_GEN, an algorithm designed to uniformly generate graphical realizations of a given joint degree matrix. Amanatidis and Kleer previously employed an MCMC-based method to address this problem. Their method fully resolved the case of two degree classes, and showed that their switch Markov chain is rapidly mixing. While our algorithm imposes certain restrictions on the maximum degrees, it is applicable to any bounded number of degree classes and has a runtime complexity linear in the number of edges.​