# Edge Representation Learning with Hypergraphs

arXiv: https://arxiv.org/abs/2106.15845 · HTML: https://mlsanity.com/paper/2106.15845/

## Key facts

- Cited by 37 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 72 references that are in the map.
- First posted on arXiv 30 Jun 2021.

## Builds on (most cited first, 30 of 39)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Modeling Relational Data with Graph Convolutional Networks](https://mlsanity.com/paper/1703.06103/) (2017)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Strategies for Pre-training Graph Neural Networks](https://mlsanity.com/paper/1905.12265/) (2019)
- [Hierarchical Graph Representation Learning with Differentiable Pooling](https://mlsanity.com/paper/1806.08804/) (2018)
- [TUDataset: A collection of benchmark datasets for learning with graphs](https://mlsanity.com/paper/2007.08663/) (2020)
- [DropEdge: Towards Deep Graph Convolutional Networks on Node Classification](https://mlsanity.com/paper/1907.10903/) (2019)
- [Benchmarking Graph Neural Networks](https://mlsanity.com/paper/2003.00982/) (2020)
- [Graph U-Nets](https://mlsanity.com/paper/1905.05178/) (2019)
- [Hypergraph Neural Networks](https://mlsanity.com/paper/1809.09401/) (2018)
- [Self-Attention Graph Pooling](https://mlsanity.com/paper/1904.08082/) (2019)
- [Composition-based Multi-Relational Graph Convolutional Networks](https://mlsanity.com/paper/1911.03082/) (2019)
- [MolGAN: An implicit generative model for small molecular graphs](https://mlsanity.com/paper/1805.11973/) (2018)
- [Learning Convolutional Neural Networks for Graphs](https://mlsanity.com/paper/1605.05273/) (2016)
- [Dynamic Edge-Conditioned Filters in Convolutional Neural Networks on Graphs](https://mlsanity.com/paper/1704.02901/) (2017)
- [Diffusion-Convolutional Neural Networks](https://mlsanity.com/paper/1511.02136/) (2015)
- [A Fair Comparison of Graph Neural Networks for Graph Classification](https://mlsanity.com/paper/1912.09893/) (2019)
- [Graph Random Neural Network for Semi-Supervised Learning on Graphs](https://mlsanity.com/paper/2005.11079/) (2020)

## Built on by (most cited first, 30 of 37)

- [Graph neural networks for materials science and chemistry](https://mlsanity.com/paper/2208.09481/) (2022)
- [Personalized Subgraph Federated Learning](https://mlsanity.com/paper/2206.10206/) (2022)
- [Multimodal learning with graphs](https://mlsanity.com/paper/2209.03299/) (2022)
- [Knowledge Graph-Augmented Language Models for Knowledge-Grounded Dialogue Generation](https://mlsanity.com/paper/2305.18846/) (2023)
- [Graph Pooling for Graph Neural Networks: Progress, Challenges, and Opportunities](https://mlsanity.com/paper/2204.07321/) (2022)
- [Equivariant Hypergraph Diffusion Neural Operators](https://mlsanity.com/paper/2207.06680/) (2022)
- [Deciphering Spatio-Temporal Graph Forecasting: A Causal Lens and Treatment](https://mlsanity.com/paper/2309.13378/) (2023)
- [Towards Self-Interpretable Graph-Level Anomaly Detection](https://mlsanity.com/paper/2310.16520/) (2023)
- [Edgeformers: Graph-Empowered Transformers for Representation Learning on Textual-Edge Networks](https://mlsanity.com/paper/2302.11050/) (2023)
- [Graph-based Approaches and Functionalities in Retrieval-Augmented Generation: A Comprehensive Survey](https://mlsanity.com/paper/2504.10499/) (2025)
- [Line Graph Contrastive Learning for Link Prediction](https://mlsanity.com/paper/2210.13795/) (2022)
- [GRATIS: Deep Learning Graph Representation with Task-specific Topology and Multi-dimensional Edge Features](https://mlsanity.com/paper/2211.12482/) (2022)
- [Molecular Hypergraph Neural Networks](https://mlsanity.com/paper/2312.13136/) (2023)
- [A Comprehensive Graph Pooling Benchmark: Effectiveness, Robustness and Generalizability](https://mlsanity.com/paper/2406.09031/) (2024)
- [Heterogeneous Graph Convolutional Neural Network via Hodge-Laplacian for Brain Functional Data](https://mlsanity.com/paper/2302.09323/) (2023)
- [Beyond the Snapshot: Brain Tokenized Graph Transformer for Longitudinal Brain Functional Connectome Embedding](https://mlsanity.com/paper/2307.00858/) (2023)
- [BOURNE: Bootstrapped Self-supervised Learning Framework for Unified Graph Anomaly Detection](https://mlsanity.com/paper/2307.15244/) (2023)
- [Dynamic Spatial-temporal Hypergraph Convolutional Network for Skeleton-based Action Recognition](https://mlsanity.com/paper/2302.08689/) (2023)
- [Graph Parsing Networks](https://mlsanity.com/paper/2402.14393/) (2024)
- [Neural Lattice Reduction: A Self-Supervised Geometric Deep Learning Approach](https://mlsanity.com/paper/2311.08170/) (2023)
- [Effective Edge-wise Representation Learning in Edge-Attributed Bipartite Graphs](https://mlsanity.com/paper/2406.13369/) (2024)
- [Self-Explaining Hypergraph Neural Networks for Diagnosis Prediction](https://mlsanity.com/paper/2502.10689/) (2025)
- [Learning Resource Allocation Policy: Vertex-GNN or Edge-GNN?](https://mlsanity.com/paper/2307.12480/) (2023)
- [Modeling Edge-Specific Node Features through Co-Representation Neural Hypergraph Diffusion](https://mlsanity.com/paper/2405.14286/) (2024)
- [Graph Neural Networks for Edge Signals: Orientation Equivariance and Invariance](https://mlsanity.com/paper/2410.16935/) (2024)
- [Enhancing Homophily-Heterophily Separation: Relation-Aware Learning in Heterogeneous Graphs](https://mlsanity.com/paper/2506.20980/) (2025)
- [Spiking Variational Graph Auto-Encoders for Efficient Graph Representation Learning](https://mlsanity.com/paper/2211.01952/) (2022)
- [GRANDE: a neural model over directed multigraphs with application to anti-money laundering](https://mlsanity.com/paper/2302.02101/) (2023)
- [Advancing Graph Neural Networks with HL-HGAT: A Hodge-Laplacian and Attention Mechanism Approach for Heterogeneous Graph-Structured Data](https://mlsanity.com/paper/2403.06687/) (2024)
- [Topological Cycle Graph Attention Network for Brain Functional Connectivity](https://mlsanity.com/paper/2403.19149/) (2024)

## Abstract (arXiv)

Graph neural networks have recently achieved remarkable success in representing graph-structured data, with rapid progress in both the node embedding and graph pooling methods. Yet, they mostly focus on capturing information from the nodes considering their connectivity, and not much work has been done in representing the edges, which are essential components of a graph. However, for tasks such as graph reconstruction and generation, as well as graph classification tasks for which the edges are important for discrimination, accurately representing edges of a given graph is crucial to the success of the graph representation learning. To this end, we propose a novel edge representation learning framework based on Dual Hypergraph Transformation (DHT), which transforms the edges of a graph into the nodes of a hypergraph. This dual hypergraph construction allows us to apply message-passing techniques for node representations to edges. After obtaining edge representations from the hypergraphs, we then cluster or drop edges to obtain holistic graph-level edge representations. We validate our edge representation learning method with hypergraphs on diverse graph datasets for graph representation and generation performance, on which our method largely outperforms existing graph representation learning methods. Moreover, our edge representation learning and pooling method also largely outperforms state-of-the-art graph pooling methods on graph classification, not only because of its accurate edge representation learning, but also due to its lossless compression of the nodes and removal of irrelevant edges for effective message-passing.