# VR-GNN: Variational Relation Vector Graph Neural Network for Modeling both Homophily and Heterophily

arXiv: https://arxiv.org/abs/2211.14523 · HTML: https://mlsanity.com/paper/2211.14523/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Nov 2022.

## Built on by (most cited first, 2 of 2)

- [The Heterophilic Graph Learning Handbook: Benchmarks, Models, Theoretical Analysis, Applications and Challenges](https://mlsanity.com/paper/2407.09618/) (2024)
- [P2GNN: Two Prototype Sets to boost GNN Performance](https://mlsanity.com/paper/2603.09195/) (2026)

## Abstract (arXiv)

Graph Neural Networks (GNNs) have achieved remarkable success in diverse real-world applications. Traditional GNNs are designed based on homophily, which leads to poor performance under heterophily scenarios. Current solutions deal with heterophily mainly by mixing high-order neighbors or passing signed messages. However, mixing high-order neighbors destroys the original graph structure and passing signed messages utilizes an inflexible message-passing mechanism, which is prone to producing unsatisfactory effects. To overcome the above problems, we propose a novel GNN model based on relation vector translation named Variational Relation Vector Graph Neural Network (VR-GNN). VR-GNN models relation generation and graph aggregation into an end-to-end model based on Variational Auto-Encoder. The encoder utilizes the structure, feature and label to generate a proper relation vector. The decoder achieves superior node representation by incorporating the relation translation into the message-passing framework. VR-GNN can fully capture the homophily and heterophily between nodes due to the great flexibility of relation translation in modeling neighbor relationships. We conduct extensive experiments on eight real-world datasets with different homophily-heterophily properties to verify the effectiveness of our model. The experimental results show that VR-GNN gains consistent and significant improvements against state-of-the-art GNN methods under heterophily, and competitive performance under homophily.