Empowering GNNs via Edge-Aware Weisfeiler-Leman Algorithm

TL;DR

This paper introduces NC-GNN, a scalable and more expressive graph neural network framework that enhances message passing by incorporating edge information, surpassing traditional 1-WL limitations.

Contribution

The paper proposes NC-1-WL and NC-GNN, extending the Weisfeiler-Leman algorithm to improve GNN expressiveness while maintaining scalability.

Findings

NC-GNN matches the power of NC-1-WL.

NC-GNN outperforms existing GNNs on benchmarks.

Theoretical expressiveness is between 1-WL and 3-WL.

Abstract

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.