Message passing graph neural networks (GNNs) are known to have their expressiveness upper-bounded by 1-dimensional Weisfeiler-Lehman (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-Lehman（1-WL）算法。为获得更强大的GNN，现有尝试要么依赖特定于任务的特征，要么涉及高时间和空间复杂度的操作。本文提出一个通用且理论上强大的GNN框架，同时保持消息传递方案的可扩展性。具体而言，我们首先通过考虑邻居间的边来增强1-WL在图同构测试中的能力，由此提出NC-1-WL。理论上，NC-1-WL的表示能力严格高于1-WL且低于3-WL。进一步，我们提出NC-GNN框架作为NC-1-WL的可微分神经网络版本。我们的简易NC-GNN实现理论上与NC-1-WL具有同等能力。实验表明，NC-GNN在多个基准测试上兼具高效性与有效性。