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We introduce a broad class of random graph models: the generalisedhypergeometric ensemble (GHypEG). This class enables to solve some longstanding problems in random graph theory. First, GHypEG provides an elegant andcompact formulation of the well-known configuration model in terms of an urnproblem. Second, GHypEG allows to incorporate arbitrary tendencies to connectdifferent vertex pairs. Third, we present the closed-form expressions of theassociated probability distribution ensures the analytical tractability of ourformulation. This is in stark contrast with the previous state-of-the-art,which is to implement the configuration model by means of computationallyexpensive procedures.

Generalised hypergeometric ensembles of random graphs: the configuration model as an urn problem