# Hyperbolic Graph Representation Learning: A Tutorial

arXiv: https://arxiv.org/abs/2211.04050 · HTML: https://mlsanity.com/paper/2211.04050/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 32 references that are in the map.
- First posted on arXiv 8 Nov 2022.

## Builds on (most cited first, 23 of 23)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/1812.08434/) (2018)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [Hyperbolic Graph Neural Networks](https://mlsanity.com/paper/1910.12892/) (2019)
- [Hyperbolic Deep Neural Networks: A Survey](https://mlsanity.com/paper/2101.04562/) (2021)
- [Constant Curvature Graph Convolutional Networks](https://mlsanity.com/paper/1911.05076/) (2019)
- [Fully Hyperbolic Neural Networks](https://mlsanity.com/paper/2105.14686/) (2021)
- [Discrete-time Temporal Network Embedding via Implicit Hierarchical Learning in Hyperbolic Space](https://mlsanity.com/paper/2107.03767/) (2021)
- [Graph Geometry Interaction Learning](https://mlsanity.com/paper/2010.12135/) (2020)
- [Hyperbolic Variational Graph Neural Network for Modeling Dynamic Graphs](https://mlsanity.com/paper/2104.02228/) (2021)
- [Latent Variable Modelling with Hyperbolic Normalizing Flows](https://mlsanity.com/paper/2002.06336/) (2020)
- [HyperML: A Boosting Metric Learning Approach in Hyperbolic Space for Recommender Systems](https://mlsanity.com/paper/1809.01703/) (2018)
- [Hyperbolic Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/2202.13852/) (2022)
- [HRCF: Enhancing Collaborative Filtering via Hyperbolic Geometric Regularization](https://mlsanity.com/paper/2204.08176/) (2022)
- [ACE-HGNN: Adaptive Curvature Exploration Hyperbolic Graph Neural Network](https://mlsanity.com/paper/2110.07888/) (2021)
- [Where are we in embedding spaces? A Comprehensive Analysis on Network Embedding Approaches for Recommender Systems](https://mlsanity.com/paper/2105.08908/) (2021)
- [HICF: Hyperbolic Informative Collaborative Filtering](https://mlsanity.com/paper/2207.09051/) (2022)
- [Hyper Meta-Path Contrastive Learning for Multi-Behavior Recommendation](https://mlsanity.com/paper/2109.02859/) (2021)
- [Enhancing Hyperbolic Graph Embeddings via Contrastive Learning](https://mlsanity.com/paper/2201.08554/) (2022)
- [Fully Hyperbolic Graph Convolution Network for Recommendation](https://mlsanity.com/paper/2108.04607/) (2021)
- [Semi-Supervised Hierarchical Drug Embedding in Hyperbolic Space](https://mlsanity.com/paper/2006.00986/) (2020)
- [Curvature Graph Generative Adversarial Networks](https://mlsanity.com/paper/2203.01604/) (2022)

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

- [Hyperbolic Representation Learning: Revisiting and Advancing](https://mlsanity.com/paper/2306.09118/) (2023)
- [kHGCN: Tree-likeness Modeling via Continuous and Discrete Curvature Learning](https://mlsanity.com/paper/2212.01793/) (2022)

## Abstract (arXiv)

Graph-structured data are widespread in real-world applications, such as social networks, recommender systems, knowledge graphs, chemical molecules etc. Despite the success of Euclidean space for graph-related learning tasks, its ability to model complex patterns is essentially constrained by its polynomially growing capacity. Recently, hyperbolic spaces have emerged as a promising alternative for processing graph data with tree-like structure or power-law distribution, owing to the exponential growth property. Different from Euclidean space, which expands polynomially, the hyperbolic space grows exponentially which makes it gains natural advantages in abstracting tree-like or scale-free graphs with hierarchical organizations. In this tutorial, we aim to give an introduction to this emerging field of graph representation learning with the express purpose of being accessible to all audiences. We first give a brief introduction to graph representation learning as well as some preliminary Riemannian and hyperbolic geometry. We then comprehensively revisit the hyperbolic embedding techniques, including hyperbolic shallow models and hyperbolic neural networks. In addition, we introduce the technical details of the current hyperbolic graph neural networks by unifying them into a general framework and summarizing the variants of each component. Moreover, we further introduce a series of related applications in a variety of fields. In the last part, we discuss several advanced topics about hyperbolic geometry for graph representation learning, which potentially serve as guidelines for further flourishing the non-Euclidean graph learning community.