# Curvature Graph Generative Adversarial Networks

arXiv: https://arxiv.org/abs/2203.01604 · HTML: https://mlsanity.com/paper/2203.01604/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 70 references that are in the map.
- First posted on arXiv 3 Mar 2022.

## Builds on (most cited first, 30 of 37)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Variational Graph Auto-Encoders](https://mlsanity.com/paper/1611.07308/) (2016)
- [Deep Graph Infomax](https://mlsanity.com/paper/1809.10341/) (2018)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [Deep Gaussian Embedding of Graphs: Unsupervised Inductive Learning via Ranking](https://mlsanity.com/paper/1707.03815/) (2017)
- [A Comprehensive Survey on Graph Anomaly Detection with Deep Learning](https://mlsanity.com/paper/2106.07178/) (2021)
- [Hyperspherical Variational Auto-Encoders](https://mlsanity.com/paper/1804.00891/) (2018)
- [Poincar'e GloVe: Hyperbolic Word Embeddings](https://mlsanity.com/paper/1810.06546/) (2018)
- [GraphGAN: Graph Representation Learning with Generative Adversarial Nets](https://mlsanity.com/paper/1711.08267/) (2017)
- [Continuous Hierarchical Representations with Poincar'e Variational Auto-Encoders](https://mlsanity.com/paper/1901.06033/) (2019)
- [Constant Curvature Graph Convolutional Networks](https://mlsanity.com/paper/1911.05076/) (2019)
- [Detection and Resolution of Rumours in Social Media: A Survey](https://mlsanity.com/paper/1704.00656/) (2017)
- [Mixed-curvature Variational Autoencoders](https://mlsanity.com/paper/1911.08411/) (2019)
- [Graph Structure Learning with Variational Information Bottleneck](https://mlsanity.com/paper/2112.08903/) (2021)
- [DeepRobust: A PyTorch Library for Adversarial Attacks and Defenses](https://mlsanity.com/paper/2005.06149/) (2020)
- [SUGAR: Subgraph Neural Network with Reinforcement Pooling and Self-Supervised Mutual Information Mechanism](https://mlsanity.com/paper/2101.08170/) (2021)
- [Spherical Latent Spaces for Stable Variational Autoencoders](https://mlsanity.com/paper/1808.10805/) (2018)
- [A Comprehensive Survey on Community Detection with Deep Learning](https://mlsanity.com/paper/2105.12584/) (2021)
- [Hyperbolic Variational Graph Neural Network for Modeling Dynamic Graphs](https://mlsanity.com/paper/2104.02228/) (2021)
- [Deep Learning for Community Detection: Progress, Challenges and Opportunities](https://mlsanity.com/paper/2005.08225/) (2020)
- [Reinforced Neighborhood Selection Guided Multi-Relational Graph Neural Networks](https://mlsanity.com/paper/2104.07886/) (2021)
- [A Self-supervised Mixed-curvature Graph Neural Network](https://mlsanity.com/paper/2112.05393/) (2021)
- [Network Geometry](https://mlsanity.com/paper/2001.03241/) (2020)
- [Adversarial Network Embedding](https://mlsanity.com/paper/1711.07838/) (2017)
- [ACE-HGNN: Adaptive Curvature Exploration Hyperbolic Graph Neural Network](https://mlsanity.com/paper/2110.07888/) (2021)

## Built on by (most cited first, 9 of 9)

- [Position-aware Structure Learning for Graph Topology-imbalance by Relieving Under-reaching and Over-squashing](https://mlsanity.com/paper/2208.08302/) (2022)
- [Hyperbolic Geometric Graph Representation Learning for Hierarchy-imbalance Node Classification](https://mlsanity.com/paper/2304.05059/) (2023)
- [Improving Heterogeneous Graph Learning with Weighted Mixed-Curvature Product Manifold](https://mlsanity.com/paper/2307.04514/) (2023)
- [Hyperbolic Graph Representation Learning: A Tutorial](https://mlsanity.com/paper/2211.04050/) (2022)
- [Torsion Graph Neural Networks](https://mlsanity.com/paper/2306.13541/) (2023)
- [HAT-GAE: Self-Supervised Graph Auto-encoders with Hierarchical Adaptive Masking and Trainable Corruption](https://mlsanity.com/paper/2301.12063/) (2023)
- [Curvature-enhanced Graph Convolutional Network for Biomolecular Interaction Prediction](https://mlsanity.com/paper/2306.13699/) (2023)
- [A roadmap for curvature-based geometric data analysis and learning](https://mlsanity.com/paper/2510.22599/) (2025)
- [Zero-shot Generalizable Graph Anomaly Detection with Mixture of Riemannian Experts](https://mlsanity.com/paper/2602.06859/) (2026)

## Abstract (arXiv)

Generative adversarial network (GAN) is widely used for generalized and robust learning on graph data. However, for non-Euclidean graph data, the existing GAN-based graph representation methods generate negative samples by random walk or traverse in discrete space, leading to the information loss of topological properties (e.g. hierarchy and circularity). Moreover, due to the topological heterogeneity (i.e., different densities across the graph structure) of graph data, they suffer from serious topological distortion problems. In this paper, we proposed a novel Curvature Graph Generative Adversarial Networks method, named modelname, which is the first GAN-based graph representation method in the Riemannian geometric manifold. To better preserve the topological properties, we approximate the discrete structure as a continuous Riemannian geometric manifold and generate negative samples efficiently from the wrapped normal distribution. To deal with the topological heterogeneity, we leverage the Ricci curvature for local structures with different topological properties, obtaining to low-distortion representations. Extensive experiments show that CurvGAN consistently and significantly outperforms the state-of-the-art methods across multiple tasks and shows superior robustness and generalization.