# Hyperbolic Graph Neural Networks: A Review of Methods and Applications

arXiv: https://arxiv.org/abs/2202.13852 · HTML: https://mlsanity.com/paper/2202.13852/

## Key facts

- Cited by 40 papers in the map (data through 14 Oct 2026).
- Builds on 69 of its 153 references that are in the map.
- First posted on arXiv 28 Feb 2022.

## Builds on (most cited first, 30 of 69)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [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)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Graph Contrastive Learning with Augmentations](https://mlsanity.com/paper/2010.13902/) (2020)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Link Prediction Based on Graph Neural Networks](https://mlsanity.com/paper/1802.09691/) (2018)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [GraphSAINT: Graph Sampling Based Inductive Learning Method](https://mlsanity.com/paper/1907.04931/) (2019)
- [Graph Contrastive Learning with Adaptive Augmentation](https://mlsanity.com/paper/2010.14945/) (2020)
- [Understanding over-squashing and bottlenecks on graphs via curvature](https://mlsanity.com/paper/2111.14522/) (2021)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [SIGN: Scalable Inception Graph Neural Networks](https://mlsanity.com/paper/2004.11198/) (2020)
- [Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry](https://mlsanity.com/paper/1806.03417/) (2018)
- [A Comprehensive Survey of Graph Embedding: Problems, Techniques and Applications](https://mlsanity.com/paper/1709.07604/) (2017)
- [Hyperbolic Graph Neural Networks](https://mlsanity.com/paper/1910.12892/) (2019)
- [A Fair Comparison of Graph Neural Networks for Graph Classification](https://mlsanity.com/paper/1912.09893/) (2019)
- [Representation Tradeoffs for Hyperbolic Embeddings](https://mlsanity.com/paper/1804.03329/) (2018)
- [Low-Dimensional Hyperbolic Knowledge Graph Embeddings](https://mlsanity.com/paper/2005.00545/) (2020)
- [Riemannian Adaptive Optimization Methods](https://mlsanity.com/paper/1810.00760/) (2018)
- [Graph Embedding Techniques, Applications, and Performance: A Survey](https://mlsanity.com/paper/1705.02801/) (2017)

## Built on by (most cited first, 30 of 40)

- [Spatio-Temporal Graph Neural Networks for Predictive Learning in Urban Computing: A Survey](https://mlsanity.com/paper/2303.14483/) (2023)
- [Hyperbolic Deep Learning in Computer Vision: A Survey](https://mlsanity.com/paper/2305.06611/) (2023)
- [Hyperbolic Fine-Tuning for Large Language Models](https://mlsanity.com/paper/2410.04010/) (2024)
- [HICF: Hyperbolic Informative Collaborative Filtering](https://mlsanity.com/paper/2207.09051/) (2022)
- [Hyperbolic Representation Learning: Revisiting and Advancing](https://mlsanity.com/paper/2306.09118/) (2023)
- [Fg-T2M++: LLMs-Augmented Fine-Grained Text Driven Human Motion Generation](https://mlsanity.com/paper/2502.05534/) (2025)
- [kHGCN: Tree-likeness Modeling via Continuous and Discrete Curvature Learning](https://mlsanity.com/paper/2212.01793/) (2022)
- [Geo-Sign: Hyperbolic Contrastive Regularisation for Geometrically Aware Sign Language Translation](https://mlsanity.com/paper/2506.00129/) (2025)
- [Dynamic Hyperbolic Attention Network for Fine Hand-object Reconstruction](https://mlsanity.com/paper/2309.02965/) (2023)
- [Hyperbolic Random Forests](https://mlsanity.com/paper/2308.13279/) (2023)
- [Bures-Wasserstein Flow Matching for Graph Generation](https://mlsanity.com/paper/2506.14020/) (2025)
- [HyperSDFusion: Bridging Hierarchical Structures in Language and Geometry for Enhanced 3D Text2Shape Generation](https://mlsanity.com/paper/2403.00372/) (2024)
- [TeleGraph: A Benchmark Dataset for Hierarchical Link Prediction](https://mlsanity.com/paper/2204.07703/) (2022)
- [BSAL: A Framework of Bi-component Structure and Attribute Learning for Link Prediction](https://mlsanity.com/paper/2204.09508/) (2022)
- [HypLL: The Hyperbolic Learning Library](https://mlsanity.com/paper/2306.06154/) (2023)
- [Hyperbolic Large Language Models](https://mlsanity.com/paper/2509.05757/) (2025)
- [Leveraging Hyperbolic Embeddings for Coarse-to-Fine Robot Design](https://mlsanity.com/paper/2311.00462/) (2023)
- [HC-GLAD: Dual Hyperbolic Contrastive Learning for Unsupervised Graph-Level Anomaly Detection](https://mlsanity.com/paper/2407.02057/) (2024)
- [Hyp-UML: Hyperbolic Image Retrieval with Uncertainty-aware Metric Learning](https://mlsanity.com/paper/2310.08390/) (2023)
- [Intrinsic Lorentz Neural Network](https://mlsanity.com/paper/2602.23981/) (2026)
- [Hyperbolic Graph Representation Learning: A Tutorial](https://mlsanity.com/paper/2211.04050/) (2022)
- [Node-Specific Space Selection via Localized Geometric Hyperbolicity in Graph Neural Networks](https://mlsanity.com/paper/2303.01724/) (2023)
- [Hyperbolic Convolution via Kernel Point Aggregation](https://mlsanity.com/paper/2306.08862/) (2023)
- [Improving Hyperbolic Representations via Gromov-Wasserstein Regularization](https://mlsanity.com/paper/2407.10495/) (2024)
- [Dynamic Portfolio Rebalancing: A Hybrid new Model Using GNNs and Pathfinding for Cost Efficiency](https://mlsanity.com/paper/2410.01864/) (2024)
- [Hyperbolic Graph Neural Networks Under the Microscope: The Role of Geometry-Task Alignment](https://mlsanity.com/paper/2602.01828/) (2026)
- [FlatLand: Personalized Graph Federated Learning via Tailored Lorentz Space](https://mlsanity.com/paper/2608.21096/) (2026)
- [FFHR: Fully and Flexible Hyperbolic Representation for Knowledge Graph Completion](https://mlsanity.com/paper/2302.04088/) (2023)
- [Improving embedding of graphs with missing data by soft manifolds](https://mlsanity.com/paper/2311.17598/) (2023)
- [Treatment-Aware Hyperbolic Representation Learning for Causal Effect Estimation with Social Networks](https://mlsanity.com/paper/2401.06557/) (2024)

## Abstract (arXiv)

Graph representation learning in Euclidean space, despite its widespread adoption and proven utility in many domains, often struggles to effectively capture the inherent hierarchical and complex relational structures prevalent in real-world data, particularly for datasets exhibiting a highly non-Euclidean latent anatomy or power-law distributions. Hyperbolic geometry, with its constant negative curvature and exponential growth property, naturally accommodates such structures, offering a promising alternative for learning rich graph representations. This survey paper provides a comprehensive review of the rapidly evolving field of Hyperbolic Graph Learning (HGL). We systematically categorize and analyze existing methods broadly dividing them into (1) hyperbolic graph embedding-based techniques, (2) graph neural network-based hyperbolic models, and (3) emerging paradigms. Beyond methodologies, we extensively discuss diverse applications of HGL across multiple domains, including recommender systems, knowledge graphs, bioinformatics, and other relevant scenarios, demonstrating the broad applicability and effectiveness of hyperbolic geometry in real-world graph learning tasks. Most importantly, we identify several key challenges that serve as directions for advancing HGL, including handling complex data structures, developing geometry-aware learning objectives, ensuring trustworthy and scalable implementations, and integrating with foundation models, e.g., large language models. We highlight promising research opportunities in this exciting interdisciplinary area. A comprehensive repository can be found at https://github.com/digailab/awesome-hyperbolic-graph-learning.