Figure 1. Illustration of directed graphlets.

(a) The 40 two- to four-node directed graphlets G₀, …, G₃₉. In each graphlet, node belonging to the same automorphism orbit are of the same colour. The 128 automorphism orbits are labelled from 0 to 127. (b) Illustration of how directed graphlets assemble together to form complex networks. The whole network can be created in three steps. First, we start with one graphlet G₁₄ (nodes a,b,c and d, in black). Then, we add a graphlet G₂ (in red) by adding two new nodes, e and f, as heads of directed edges from node b. Finally, we add a graphlet G₄ (in blue) by adding a new node, g, as the head of a directed edge from node d and as the tail of a directed edge towards node c. Note that during this process, many new graphlets are created, e.g., graphlet G₃ (in green) between nodes b, c and g. (c) Illustration of our anti-parallel directed edge counting strategy. The two anti-parallel directed edges in the input network (in blue and in magenta) account for one graphlet G₂₁ (when considering the magenta directed edge) and one graphlet G₂₅ (when considering the blue directed edge), among all other induced graphlets.