  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.
