# Hyperbolic Variational Graph Neural Network for Modeling Dynamic Graphs

arXiv: https://arxiv.org/abs/2104.02228 · HTML: https://mlsanity.com/paper/2104.02228/

## Key facts

- Cited by 50 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 46 references that are in the map.
- First posted on arXiv 6 Apr 2021.

## Builds on (most cited first, 24 of 24)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [LINE: Large-scale Information Network Embedding](https://mlsanity.com/paper/1503.03578/) (2015)
- [Inductive Representation Learning on Temporal Graphs](https://mlsanity.com/paper/2002.07962/) (2020)
- [Predicting Dynamic Embedding Trajectory in Temporal Interaction Networks](https://mlsanity.com/paper/1908.01207/) (2019)
- [EvolveGCN: Evolving Graph Convolutional Networks for Dynamic Graphs](https://mlsanity.com/paper/1902.10191/) (2019)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry](https://mlsanity.com/paper/1806.03417/) (2018)
- [Hyperbolic Graph Neural Networks](https://mlsanity.com/paper/1910.12892/) (2019)
- [Poincar'e GloVe: Hyperbolic Word Embeddings](https://mlsanity.com/paper/1810.06546/) (2018)
- [Multi-relational Poincar'e Graph Embeddings](https://mlsanity.com/paper/1905.09791/) (2019)
- [Hyperbolic Attention Networks](https://mlsanity.com/paper/1805.09786/) (2018)
- [Continuous Graph Neural Networks](https://mlsanity.com/paper/1912.00967/) (2019)
- [Continuous Hierarchical Representations with Poincar'e Variational Auto-Encoders](https://mlsanity.com/paper/1901.06033/) (2019)
- [Variational Graph Recurrent Neural Networks](https://mlsanity.com/paper/1908.09710/) (2019)
- [Hierarchical Taxonomy-Aware and Attentional Graph Capsule RCNNs for Large-Scale Multi-Label Text Classification](https://mlsanity.com/paper/1906.04898/) (2019)
- [Hyperbolic Representation Learning for Fast and Efficient Neural Question Answering](https://mlsanity.com/paper/1707.07847/) (2017)
- [DNA: Dynamic Social Network Alignment](https://mlsanity.com/paper/1911.00067/) (2019)

## Built on by (most cited first, 30 of 50)

- [Hyperbolic Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/2202.13852/) (2022)
- [LLM4DyG: Can Large Language Models Solve Spatial-Temporal Problems on Dynamic Graphs?](https://mlsanity.com/paper/2310.17110/) (2023)
- [RiemannGFM: Learning a Graph Foundation Model from Riemannian Geometry](https://mlsanity.com/paper/2502.03251/) (2025)
- [A Self-supervised Mixed-curvature Graph Neural Network](https://mlsanity.com/paper/2112.05393/) (2021)
- [Self-Supervised Continual Graph Learning in Adaptive Riemannian Spaces](https://mlsanity.com/paper/2211.17068/) (2022)
- [ACE-HGNN: Adaptive Curvature Exploration Hyperbolic Graph Neural Network](https://mlsanity.com/paper/2110.07888/) (2021)
- [A Self-supervised Riemannian GNN with Time Varying Curvature for Temporal Graph Learning](https://mlsanity.com/paper/2208.14073/) (2022)
- [Motif-aware Riemannian Graph Neural Network with Generative-Contrastive Learning](https://mlsanity.com/paper/2401.01232/) (2024)
- [Uncertainty in Graph Neural Networks: A Survey](https://mlsanity.com/paper/2403.07185/) (2024)
- [Graph Neural Networks Designed for Different Graph Types: A Survey](https://mlsanity.com/paper/2204.03080/) (2022)
- [Hyperbolic Representation Learning: Revisiting and Advancing](https://mlsanity.com/paper/2306.09118/) (2023)
- [LSEnet: Lorentz Structural Entropy Neural Network for Deep Graph Clustering](https://mlsanity.com/paper/2405.11801/) (2024)
- [Hyperbolic Geometric Latent Diffusion Model for Graph Generation](https://mlsanity.com/paper/2405.03188/) (2024)
- [Spectral Invariant Learning for Dynamic Graphs under Distribution Shifts](https://mlsanity.com/paper/2403.05026/) (2024)
- [DeepRicci: Self-supervised Graph Structure-Feature Co-Refinement for Alleviating Over-squashing](https://mlsanity.com/paper/2401.12780/) (2024)
- [Spiking Graph Neural Network on Riemannian Manifolds](https://mlsanity.com/paper/2410.17941/) (2024)
- [Contrastive Graph Clustering in Curvature Spaces](https://mlsanity.com/paper/2305.03555/) (2023)
- [HGWaveNet: A Hyperbolic Graph Neural Network for Temporal Link Prediction](https://mlsanity.com/paper/2304.07302/) (2023)
- [BotDGT: Dynamicity-aware Social Bot Detection with Dynamic Graph Transformers](https://mlsanity.com/paper/2404.15070/) (2024)
- [Curvature Graph Generative Adversarial Networks](https://mlsanity.com/paper/2203.01604/) (2022)
- [Hyperbolic Random Forests](https://mlsanity.com/paper/2308.13279/) (2023)
- [Autoencoding Hyperbolic Representation for Adversarial Generation](https://mlsanity.com/paper/2201.12825/) (2022)
- [Variational Graph Generator for Multi-View Graph Clustering](https://mlsanity.com/paper/2210.07011/) (2022)
- [WL-Align: Weisfeiler-Lehman Relabeling for Aligning Users across Networks via Regularized Representation Learning](https://mlsanity.com/paper/2212.14182/) (2022)
- [Deeper with Riemannian Geometry: Overcoming Oversmoothing and Oversquashing for Graph Foundation Models](https://mlsanity.com/paper/2510.17457/) (2025)
- [Spectro-Riemannian Graph Neural Networks](https://mlsanity.com/paper/2502.00401/) (2025)
- [Out-of-Distribution Generalized Dynamic Graph Neural Network for Human Albumin Prediction](https://mlsanity.com/paper/2311.15545/) (2023)
- [SINCERE: Sequential Interaction Networks representation learning on Co-Evolving RiEmannian manifolds](https://mlsanity.com/paper/2305.03883/) (2023)
- [Uncertainty Quantification on Graph Learning: A Survey](https://mlsanity.com/paper/2404.14642/) (2024)
- [Towards Scalable Hyperbolic Neural Networks using Taylor Series Approximations](https://mlsanity.com/paper/2206.03610/) (2022)

## Abstract (arXiv)

Learning representations for graphs plays a critical role in a wide spectrum of downstream applications. In this paper, we summarize the limitations of the prior works in three folds: representation space, modeling dynamics and modeling uncertainty. To bridge this gap, we propose to learn dynamic graph representation in hyperbolic space, for the first time, which aims to infer stochastic node representations. Working with hyperbolic space, we present a novel Hyperbolic Variational Graph Neural Network, referred to as HVGNN. In particular, to model the dynamics, we introduce a Temporal GNN (TGNN) based on a theoretically grounded time encoding approach. To model the uncertainty, we devise a hyperbolic graph variational autoencoder built upon the proposed TGNN to generate stochastic node representations of hyperbolic normal distributions. Furthermore, we introduce a reparameterisable sampling algorithm for the hyperbolic normal distribution to enable the gradient-based learning of HVGNN. Extensive experiments show that HVGNN outperforms state-of-the-art baselines on real-world datasets.