# A Novel Higher-order Weisfeiler-Lehman Graph Convolution

arXiv: https://arxiv.org/abs/2007.00346 · HTML: https://mlsanity.com/paper/2007.00346/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jul 2020.

## Built on by (most cited first, 10 of 10)

- [Expressiveness and Approximation Properties of Graph Neural Networks](https://mlsanity.com/paper/2204.04661/) (2022)
- [Graph Neural Networks with Local Graph Parameters](https://mlsanity.com/paper/2106.06707/) (2021)
- [A Short Tutorial on The Weisfeiler-Lehman Test And Its Variants](https://mlsanity.com/paper/2201.07083/) (2022)
- [Theoretically Improving Graph Neural Networks via Anonymous Walk Graph Kernels](https://mlsanity.com/paper/2104.02995/) (2021)
- [Strong Transitivity Relations and Graph Neural Networks](https://mlsanity.com/paper/2401.01384/) (2024)
- [Torsion Graph Neural Networks](https://mlsanity.com/paper/2306.13541/) (2023)
- [Rethinking Performance Measures of RNA Secondary Structure Problems](https://mlsanity.com/paper/2401.05351/) (2023)
- [CUQ-GNN: Committee-based Graph Uncertainty Quantification using Posterior Networks](https://mlsanity.com/paper/2409.04159/) (2024)
- [PersonaSAGE: A Multi-Persona Graph Neural Network](https://mlsanity.com/paper/2212.13709/) (2022)
- [A Structural Approach to the Design of Domain Specific Neural Network Architectures](https://mlsanity.com/paper/2301.09381/) (2023)

## Abstract (arXiv)

Current GNN architectures use a vertex neighborhood aggregation scheme, which limits their discriminative power to that of the 1-dimensional Weisfeiler-Lehman (WL) graph isomorphism test. Here, we propose a novel graph convolution operator that is based on the 2-dimensional WL test. We formally show that the resulting 2-WL-GNN architecture is more discriminative than existing GNN approaches. This theoretical result is complemented by experimental studies using synthetic and real data. On multiple common graph classification benchmarks, we demonstrate that the proposed model is competitive with state-of-the-art graph kernels and GNNs.