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Message passing graph neural networks (GNNs) are known to have theirexpressiveness upper-bounded by 1-dimensional Weisfeiler-Leman (1-WL)algorithm. To achieve more powerful GNNs, existing attempts either require adhoc features, or involve operations that incur high time and spacecomplexities. In this work, we propose a general and provably powerful GNNframework that preserves the scalability of the message passing scheme. Inparticular, we first propose to empower 1-WL for graph isomorphism test byconsidering edges among neighbors, giving rise to NC-1-WL. The expressivenessof 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 ofNC-1-WL. Our simple implementation of NC-GNN is provably as powerful asNC-1-WL. Experiments demonstrate that our NC-GNN performs effectively andefficiently on various benchmarks.

Empowering GNNs via Edge-Aware Weisfeiler-Leman Algorithm