# Hyperbolic Node Embedding for Signed Networks

arXiv: https://arxiv.org/abs/1910.13090 · HTML: https://mlsanity.com/paper/1910.13090/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Oct 2019.

## Built on by (most cited first, 6 of 6)

- [Dual Space Graph Contrastive Learning](https://mlsanity.com/paper/2201.07409/) (2022)
- [Survey of Generative Methods for Social Media Analysis](https://mlsanity.com/paper/2112.07041/) (2021)
- [SigGAN : Adversarial Model for Learning Signed Relationships in Networks](https://mlsanity.com/paper/2201.06437/) (2022)
- [Towards LLM-Empowered Knowledge Tracing via LLM-Student Hierarchical Behavior Alignment in Hyperbolic Space](https://mlsanity.com/paper/2602.22879/) (2026)
- [Signed-Graph Recommendation as Structural Consistency Maximization](https://mlsanity.com/paper/2607.05952/) (2026)
- [Polarity-Asymmetric Structural Calibration for Link Sign Prediction](https://mlsanity.com/paper/2609.05896/) (2026)

## Abstract (arXiv)

Signed network embedding methods aim to learn vector representations of nodes in signed networks. However, existing algorithms only managed to embed networks into low-dimensional Euclidean spaces whereas many intrinsic features of signed networks are reported more suitable for non-Euclidean spaces. For instance, previous works did not consider the hierarchical structures of networks, which is widely witnessed in real-world networks. In this work, we answer an open question that whether the hyperbolic space is a better choice to accommodate signed networks and learn embeddings that can preserve the corresponding special characteristics. We also propose a non-Euclidean signed network embedding method based on structural balance theory and Riemannian optimization, which embeds signed networks into a Poincar'e ball in a hyperbolic space. This space enables our approach to capture underlying hierarchy of nodes in signed networks because it can be seen as a continuous tree. We empirically compare our method against six Euclidean-based baselines in three tasks on seven real-world datasets, and the results show the effectiveness of our method.