Supplementary Material: C–GRAAL: Common–Neighbors–Based Global GRAph ALignment of Biological Networks†

To determine topological similarity between two nodes in different networks, we use the similarity measure of nodes’ local neighborhoods, as described by Milenković and Pržulj1. This measure generalizes the degree of a node, which counts the number of edges that the node touches, into the vector of graphlet degrees, that counts the number of graphlets that the node touches, for all 2-5-node graphlets. A graphlet is a small connected induced subgraph of a large network (e.g., an edge, a 3-node path, a triangle, etc.)3. Since it is topologically relevant to distinguish between, for example, nodes touching a 3-node path at an end or at the middle, the notion of automorphism orbits (or just orbits, for brevity) is used. By taking into account the “symmetries” between nodes of a graphlet, there are 73 different orbits across all 2to 5-node graphlets. The full vector of 73 coordinates is the graphlet degree vector of a node that captures the node’s interconnectivities out to a distance of 4 (see1 for details). Topological similarity between two nodes in different networks is computed as follows. For a node u, ui denotes the ith coordinate of its graphlet degree vector, i.e., ui is the number of times node u touches an orbit i. The distance Di(u,v) between the ith orbits of nodes u and v is defined as: Di(u,v) = wi× |log(ui+1)−log(vi+1)| log(max{ui,vi}+2) , where wi is a weight of orbit i signifying its “importance” (see1 for details). The total distance D(u,v) between nodes u and v is defined as: