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We develop random graph models where graphs are generated by connecting not only pairs of vertices by edges, but also larger subsets of vertices by copies of small atomic subgraphs of arbitrary topology. This allows for the generation of graphs with extensive numbers of triangles and other network motifs commonly observed in many real-world networks. More specifically, we focus on maximum entropy ensembles under constraints placed on the counts and distributions of atomic subgraphs and derive general expressions for the entropy of such mo