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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.
Advancing our understanding of human behavior hinges on the ability of theories to unveil the mechanisms underlying such behaviors. Measuring the ability of theories and models to predict unobserved behaviors provides a principled method to evaluate
Mesoscopic pattern extraction (MPE) is the problem of finding a partition of the nodes of a complex network that maximizes some objective function. Many well-known network inference problems fall in this category, including, for instance, community d
As new instances of nested organization --beyond ecological networks-- are discovered, scholars are debating around the co-existence of two apparently incompatible macroscale architectures: nestedness and modularity. The discussion is far from being
Maximum entropy null models of networks come in different flavors that depend on the type of constraints under which entropy is maximized. If the constraints are on degree sequences or distributions, we are dealing with configuration models. If the d
A preferential attachment model for a growing network incorporating deletion of edges is studied and the expected asymptotic degree distribution is analyzed. At each time step $t=1,2,ldots$, with probability $pi_1>0$ a new vertex with one edge attach