We provide a novel family of generative block-models for random graphs that naturally incorporates degree distributions: the block-constrained configuration model. Block-constrained configuration models build on the generalized hypergeometric ensemble of random graphs and extend the well-known configuration model by enforcing block-constraints on the edge-generating process. The resulting models are practical to fit even to large networks. These models provide a new, flexible tool for the study of community structure and for network science in general, where modeling networks with heterogeneous degree distributions is of central importance.

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