# Link prediction with hyperbolic geometry

arXiv: https://arxiv.org/abs/1903.08810 · HTML: https://mlsanity.com/paper/1903.08810/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Mar 2019.

## Built on by (most cited first, 7 of 7)

- [Zoo Guide to Network Embedding](https://mlsanity.com/paper/2305.03474/) (2023)
- [Hyperbolic Graph Neural Networks Under the Microscope: The Role of Geometry-Task Alignment](https://mlsanity.com/paper/2602.01828/) (2026)
- [Reconstruction of Random Geometric Graphs: Breaking the Omega(r) distortion barrier](https://mlsanity.com/paper/2107.14323/) (2021)
- [Symmetry-driven embedding of networks in hyperbolic space](https://mlsanity.com/paper/2406.10711/) (2024)
- [Leveraging Non-linear Dimension Reduction and Random Walk Co-occurrence for Node Embedding](https://mlsanity.com/paper/2602.24069/) (2026)
- [Bayesian Latent Space Models for Graphs Are Misspecified: Toward Robust Inference via Generalized Posteriors](https://mlsanity.com/paper/2605.18927/) (2026)
- [Hyperbolic Graph Embedders for Link Prediction and Topology Reconstruction](https://mlsanity.com/paper/2608.07029/) (2026)

## Abstract (arXiv)

Link prediction is a paradigmatic problem in network science with a variety of applications. In latent space network models this problem boils down to ranking pairs of nodes in the order of increasing latent distances between them. The network model with hyperbolic latent spaces has a number of attractive properties suggesting it must be a powerful tool to predict links, but the past work in this direction reported mixed results. Here we perform systematic investigation of the utility of latent hyperbolic geometry for link prediction in networks. We first show that some measures of link prediction accuracy are extremely sensitive with respect to inaccuracies in the inference of latent hyperbolic coordinates of nodes, so that we develop a new coordinate inference method that maximizes the accuracy of such inference. Applying this method to synthetic and real networks, we then find that while there exists a multitude of competitive methods to predict obvious easy-to-predict links, among which hyperbolic link prediction is rarely the best but often competitive, it is the best, often by far, when the task is to predict less obvious missing links that are really hard to predict. These links include missing links in incomplete networks with large fractions of missing links, missing links between nodes that do not have any common neighbors, and missing links between dissimilar nodes at large latent distances. Overall these results suggest that the harder a specific link prediction task is, the more seriously one should consider using hyperbolic geometry.