Graph Neural Networks (GNNs) are widely used for graph representation learning in many application domains. The expressiveness of vanilla GNNs is upper-bounded by 1-dimensional Weisfeiler-Leman (1-WL) test as they operate on rooted subtrees through iterative message passing. In this paper, we empower GNNs by injecting neighbor-connectivity information extracted from a new type of substructure. 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 1-hop neighborhood of an edge. 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. Additionally, the local encoding from union subgraphs can also be injected into arbitrary message-passing neural networks (MPNNs) and Transformer-based models as a plugin. Extensive experiments on 18 benchmarks of both graph-level and node-level tasks demonstrate that UnionSNN outperforms state-of-the-art baseline models, with competitive computational efficiency. The injection of our local encoding to existing models is able to boost the performance by up to 11.09%. Our code is available at https://github.com/AngusMonroe/UnionSNN.

翻译：图神经网络（GNN）被广泛应用于众多应用领域的图表示学习。由于原始GNN通过迭代消息传递在根子树结构上运行，其表达能力受限于一维Weisfeiler-Leman（1-WL）测试。本文通过注入从新型子结构中提取的邻居连接性信息来增强GNN的能力。我们首先探讨了局部邻域中存在的不同连接类型，识别出一种称为联合子图的子结构，该结构能够完整刻画一条边的1跳邻域全貌。随后设计了一种基于最短路径的子结构描述符，该描述符具有三个优良性质，能有效编码联合子图中的高阶连接性。通过注入编码后的邻居连接性，我们提出了一种新型模型——联合子图神经网络（UnionSNN），该模型被证明在区分非同构图方面严格强于1-WL测试。此外，从联合子图中提取的局部编码可作为插件注入任意消息传递神经网络（MPNN）和基于Transformer的模型中。在18个图级和节点级任务基准上的广泛实验表明，UnionSNN以具有竞争力的计算效率超越了当前最先进的基线模型。将我们的局部编码注入现有模型可使性能提升最高达11.09%。我们的代码开源在https://github.com/AngusMonroe/UnionSNN。