# Quaternion Graph Neural Networks

arXiv: https://arxiv.org/abs/2008.05089 · HTML: https://mlsanity.com/paper/2008.05089/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Aug 2020.

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

- [Clifford Neural Layers for PDE Modeling](https://mlsanity.com/paper/2209.04934/) (2022)
- [ReGVD: Revisiting Graph Neural Networks for Vulnerability Detection](https://mlsanity.com/paper/2110.07317/) (2021)
- [Node Co-occurrence based Graph Neural Networks for Knowledge Graph Link Prediction](https://mlsanity.com/paper/2104.07396/) (2021)
- [Convolutional Filtering and Neural Networks with Non Commutative Algebras](https://mlsanity.com/paper/2108.09923/) (2021)
- [Parameterized Hypercomplex Graph Neural Networks for Graph Classification](https://mlsanity.com/paper/2103.16584/) (2021)
- [Graph Learning in 4D: a Quaternion-valued Laplacian to Enhance Spectral GCNs](https://mlsanity.com/paper/2312.17361/) (2023)
- [Two-view Graph Neural Networks for Knowledge Graph Completion](https://mlsanity.com/paper/2112.09231/) (2021)
- [Demystifying the Hypercomplex: Inductive Biases in Hypercomplex Deep Learning](https://mlsanity.com/paper/2405.07024/) (2024)
- [Quaternion-Based Graph Convolution Network for Recommendation](https://mlsanity.com/paper/2111.10536/) (2021)
- [Graph Neural Networks at a Fraction](https://mlsanity.com/paper/2502.06136/) (2025)

## Abstract (arXiv)

Recently, graph neural networks (GNNs) have become an important and active research direction in deep learning. It is worth noting that most of the existing GNN-based methods learn graph representations within the Euclidean vector space. Beyond the Euclidean space, learning representation and embeddings in hyper-complex space have also shown to be a promising and effective approach. To this end, we propose Quaternion Graph Neural Networks (QGNN) to learn graph representations within the Quaternion space. As demonstrated, the Quaternion space, a hyper-complex vector space, provides highly meaningful computations and analogical calculus through Hamilton product compared to the Euclidean and complex vector spaces. Our QGNN obtains state-of-the-art results on a range of benchmark datasets for graph classification and node classification. Besides, regarding knowledge graphs, our QGNN-based embedding model achieves state-of-the-art results on three new and challenging benchmark datasets for knowledge graph completion. Our code is available at: urlhttps://github.com/daiquocnguyen/QGNN.