Message passing graph neural networks (GNNs) are known to have their expressiveness upper-bounded by 1-dimensional Weisfeiler-Leman (1-WL) algorithm. To achieve more powerful GNNs, existing attempts either require ad hoc features, or involve operations that incur high time and space complexities. In this work, we propose a general and provably powerful GNN framework that preserves the scalability of the message passing scheme. In particular, we first propose to empower 1-WL for graph isomorphism test by considering edges among neighbors, giving rise to NC-1-WL. The expressiveness of NC-1-WL is shown to be strictly above 1-WL and below 3-WL theoretically. Further, we propose the NC-GNN framework as a differentiable neural version of NC-1-WL. Our simple implementation of NC-GNN is provably as powerful as NC-1-WL. Experiments demonstrate that our NC-GNN performs effectively and efficiently on various benchmarks.

翻译：消息传递图神经网络（GNN）的表示能力已知受限于一维Weisfeiler-Leman（1-WL）算法。为构建更强表达能力的GNN，现有方法要么需要特定设计的特征，要么涉及高时间复杂度和空间复杂度的操作。本文提出一个通用且可证明强表达能力的GNN框架，同时保留消息传递机制的可扩展性。具体而言，我们首先通过考虑邻居节点间的边关系来增强1-WL的图同构测试能力，由此提出NC-1-WL算法。理论上证明NC-1-WL的表达能力严格强于1-WL且弱于3-WL。进一步，我们提出NC-GNN框架作为NC-1-WL的可微分神经实现。我们简化实现的NC-GNN在理论上具有与NC-1-WL同等的表达能力。实验表明，NC-GNN在多个基准测试上实现了高效且有效的性能。