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