  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
generalised hypergeometric ensemble of random graphs and extend the well-known
configuration model by enforcing block-constraints on the edge generation
process. The resulting models are analytically tractable and 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 modelling
networks with heterogeneous degree distributions is of central importance.
