Title: Union Subgraph Neural Networks. Abstract: Graph Neural Networks (GNNs) are widely used for graph representation learning in many application domains. The expressiveness of GNNs is upper-bounded by 1-dimensional Weisfeiler-Lehman (1-WL) test as they operate on rooted subtrees in message passing. In this paper, we empower GNNs by injecting neighbor-connectivity information extracted from a new type of substructures. We first investigate different kinds of connectivities existing in a local neighborhood and identify a substructure called union subgraph, which is able to capture the complete picture of the neighborhood. We then design a shortest-path-based substructure descriptor that possesses three nice properties and can effectively encode the high-order connectivities in union subgraphs. By infusing the encoded neighbor connectivities, we propose a novel model, namely Union Subgraph Neural Network (UnionSNN), which is proven to be strictly more powerful than 1-WL in distinguishing non-isomorphic graphs. Our extensive experiments on both graph-level and node-level classification tasks demonstrate that UnionSNN outperforms state-of-the-art baseline models, with competitive computational efficiency.
