  Link prediction is an important learning task for graph-structured data. In
this paper, we propose a novel topological approach to characterize
interactions between two nodes. Our topological feature, based on the extended
persistence homology, encodes rich structural information regarding the
multi-hop paths connecting nodes. Based on this feature, we propose a graph
neural network method that outperforms state-of-the-arts on different
benchmarks. As another contribution, we propose a novel algorithm to more
efficiently compute the extended persistent diagrams for graphs. This algorithm
can be generally applied to accelerate many other topological methods for graph
learning tasks.
