Being able to generate large synthetic graphs resembling those found in the real world, is of high importance for the design of new graph algorithms and benchmarks. In this paper, we first compare several probability models in terms of goodness-of-fit, when used to model the degree distribution of real graphs. Second, after confirming that the MOEZipf model is the one that gives better fits, we present a method to generate MOEZipf distributions. The method is shown to work well in practice when implemented in a scalable synthetic graph generator.