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Because of the huge number of graphs possible even with a small number ofnodes, inference on network structure is known to be a challenging problem.Generating large random directed graphs with prescribed probabilities ofoccurrences of some meaningful patterns (motifs) is also difficult. We show howto generate such random graphs according to a formal probabilisticrepresentation, using fast Markov chain Monte Carlo methods to sample them. Asan illustration, we generate realistic graphs with several hundred nodesmimicking a gene transcription interaction network in Escherichia coli.

Probabilistic generation of random networks taking into account information on motifs occurrence