From homogeneous to heterogeneous network alignment via colored graphlets.

Network alignment (NA) compares networks with the goal of finding a node mapping that uncovers highly similar (conserved) network regions. Existing NA methods are homogeneous, i.e., they can deal only with networks containing nodes and edges of one type. Due to increasing amounts of heterogeneous network data with nodes or edges of different types, we extend three recent state-of-the-art homogeneous NA methods, WAVE, MAGNA++, and SANA, to allow for heterogeneous NA for the first time. We introduce several algorithmic novelties. Namely, these existing methods compute homogeneous graphlet-based node similarities and then find high-scoring alignments with respect to these similarities, while simultaneously maximizing the amount of conserved edges. Instead, we extend homogeneous graphlets to their heterogeneous counterparts, which we then use to develop a new measure of heterogeneous node similarity. Also, we extend S3, a state-of-the-art measure of edge conservation for homogeneous NA, to its heterogeneous counterpart. Then, we find high-scoring alignments with respect to our heterogeneous node similarity and edge conservation measures. In evaluations on synthetic and real-world biological networks, our proposed heterogeneous NA methods lead to higher-quality alignments and better robustness to noise in the data than their homogeneous counterparts. The software and data from this work is available at https://nd.edu/~cone/colored_graphlets/.