Generalized Gromov Wasserstein Distance for Seed-Informed Network Alignment

Network alignment is a commonly encountered problem in many applications, where the objective is to match the nodes in different networks such that the incident edges of matched nodes are consistent. Gromov-Wasserstein (GW) distance, based on optimal transport, has been shown to be useful in assessing the topological (dis)similarity between two networks, as well as network alignment. In many practical applications of network alignment, there may be "seed" nodes with known matchings. However, GW distance assumes that no matchings are known. Here, we propose Generalized GW-based Network Alignment(GGWNA), with a loss/distance function that reflects the topological similarity of known matching nodes. We test the resulting framework using a large collection of real-world social networks. Our results show that, as compared to state-of-the-art network alignment algorithms, GGWNA can deliver more accurate alignment when the seed size is small. We also perform systematic simulation studies to characterize the performance of GGWNA as a function of seed size and noise, and find that GGWNA is more robust to noise as compared to competing algorithms. The implementation of GGWNA and the Supplementary Material can be found in https://github.com/Meng- zhen-Li/Generalized-GW.git.