# Hypergraph Convolutional Networks via Equivalency between Hypergraphs and Undirected Graphs

arXiv: https://arxiv.org/abs/2203.16939 · HTML: https://mlsanity.com/paper/2203.16939/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 46 of its 117 references that are in the map.
- First posted on arXiv 31 Mar 2022.

## Builds on (most cited first, 30 of 46)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (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)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Simple and Deep Graph Convolutional Networks](https://mlsanity.com/paper/2007.02133/) (2020)
- [Multi-view Convolutional Neural Networks for 3D Shape Recognition](https://mlsanity.com/paper/1505.00880/) (2015)
- [Revisiting Point Cloud Classification: A New Benchmark Dataset and Classification Model on Real-World Data](https://mlsanity.com/paper/1908.04616/) (2019)
- [Hypergraph Neural Networks](https://mlsanity.com/paper/1809.09401/) (2018)
- [PairNorm: Tackling Oversmoothing in GNNs](https://mlsanity.com/paper/1909.12223/) (2019)
- [Evaluating Protein Transfer Learning with TAPE](https://mlsanity.com/paper/1906.08230/) (2019)
- [PAConv: Position Adaptive Convolution with Dynamic Kernel Assembling on Point Clouds](https://mlsanity.com/paper/2103.14635/) (2021)
- [UniGNN: a Unified Framework for Graph and Hypergraph Neural Networks](https://mlsanity.com/paper/2105.00956/) (2021)
- [You are AllSet: A Multiset Function Framework for Hypergraph Neural Networks](https://mlsanity.com/paper/2106.13264/) (2021)
- [Higher-order organization of complex networks](https://mlsanity.com/paper/1612.08447/) (2016)
- [HNHN: Hypergraph Networks with Hyperedge Neurons](https://mlsanity.com/paper/2006.12278/) (2020)
- [Interpolated Convolutional Networks for 3D Point Cloud Understanding](https://mlsanity.com/paper/1908.04512/) (2019)
- [Be More with Less: Hypergraph Attention Networks for Inductive Text Classification](https://mlsanity.com/paper/2011.00387/) (2020)
- [Directed Graph Convolutional Network](https://mlsanity.com/paper/2004.13970/) (2020)
- [Hyper-SAGNN: a self-attention based graph neural network for hypergraphs](https://mlsanity.com/paper/1911.02613/) (2019)
- [MotifNet: a motif-based Graph Convolutional Network for directed graphs](https://mlsanity.com/paper/1802.01572/) (2018)
- [HyperSAGE: Generalizing Inductive Representation Learning on Hypergraphs](https://mlsanity.com/paper/2010.04558/) (2020)
- [Edge Contraction Pooling for Graph Neural Networks](https://mlsanity.com/paper/1905.10990/) (2019)
- [Learning protein sequence embeddings using information from structure](https://mlsanity.com/paper/1902.08661/) (2019)

## Built on by (most cited first, 16 of 16)

- [Equivariant Hypergraph Diffusion Neural Operators](https://mlsanity.com/paper/2207.06680/) (2022)
- [A Survey on Hypergraph Neural Networks: An In-Depth and Step-By-Step Guide](https://mlsanity.com/paper/2404.01039/) (2024)
- [I'm Me, We're Us, and I'm Us: Tri-directional Contrastive Learning on Hypergraphs](https://mlsanity.com/paper/2206.04739/) (2022)
- [From Hypergraph Energy Functions to Hypergraph Neural Networks](https://mlsanity.com/paper/2306.09623/) (2023)
- [GraphTTA: Test Time Adaptation on Graph Neural Networks](https://mlsanity.com/paper/2208.09126/) (2022)
- [A Hypergraph Neural Network Framework for Learning Hyperedge-Dependent Node Embeddings](https://mlsanity.com/paper/2212.14077/) (2022)
- [CAT-Walk: Inductive Hypergraph Learning via Set Walks](https://mlsanity.com/paper/2306.11147/) (2023)
- [SubGDiff: A Subgraph Diffusion Model to Improve Molecular Representation Learning](https://mlsanity.com/paper/2405.05665/) (2024)
- [Ada-HGNN: Adaptive Sampling for Scalable Hypergraph Neural Networks](https://mlsanity.com/paper/2405.13372/) (2024)
- [Demystifying Higher-Order Graph Neural Networks](https://mlsanity.com/paper/2406.12841/) (2024)
- [Directional Sheaf Hypergraph Networks: Unifying Learning on Directed and Undirected Hypergraphs](https://mlsanity.com/paper/2510.04727/) (2025)
- [HyperMagNet: A Magnetic Laplacian based Hypergraph Neural Network](https://mlsanity.com/paper/2402.09676/) (2024)
- [A Simple Hypergraph Kernel Convolution based on Discounted Markov Diffusion Process](https://mlsanity.com/paper/2210.16884/) (2022)
- [Graph Augmentation for Cross Graph Domain Generalization](https://mlsanity.com/paper/2502.18188/) (2025)
- [Attention-based graph neural networks: a survey](https://mlsanity.com/paper/2605.08679/) (2026)
- [PANDA: Prior-guided Attentional Dual-path Architecture](https://mlsanity.com/paper/2610.13635/) (2026)

## Abstract (arXiv)

As a powerful tool for modeling complex relationships, hypergraphs are gaining popularity from the graph learning community. However, commonly used frameworks in deep hypergraph learning focus on hypergraphs with edge-independent vertex weights (EIVWs), without considering hypergraphs with edge-dependent vertex weights (EDVWs) that have more modeling power. To compensate for this, we present General Hypergraph Spectral Convolution (GHSC), a general learning framework that not only handles EDVW and EIVW hypergraphs, but more importantly, enables theoretically explicitly utilizing the existing powerful Graph Convolutional Neural Networks (GCNNs) such that largely ease the design of Hypergraph Neural Networks. In this framework, the graph Laplacian of the given undirected GCNNs is replaced with a unified hypergraph Laplacian that incorporates vertex weight information from a random walk perspective by equating our defined generalized hypergraphs with simple undirected graphs. Extensive experiments from various domains including social network analysis, visual objective classification, and protein learning demonstrate the state-of-the-art performance of the proposed framework.