The topology of undirected biological networks, such as protein-protein interaction networks, or genetic interaction networks, has been extensively explored in search of new biological knowledge. Graphlets, small connected non-isomorphic induced sub-graphs of an undirected network, have been particularly useful in computational network biology. Having in mind that a significant portion of biological networks, such as metabolic networks or
transcriptional regulatory networks, are directed by nature, we define all up to four node directed graphlets and orbits and implement the directed graphlet and graphlet orbits counting algorithm. We generalise all existing graphlet based measures to the directed case, defining: relative directed graphlet frequency distance, directed graphlet degree distribution similarity,
directed graphlet degree vector similarity, and directed graphlet correlation distance. We apply new topological measures to metabolic networks and show that the topology of directed biological networks is correlated with
biological function. Finally, we look for topology–function relationships in metabolic networks that are conserved across different species.