Hyperbolic Graph Embedders for Link Prediction and Topology Reconstruction

2026-08-07

AI Summary

This study addresses the lack of systematic evaluation of hyperbolic graph embedding methods for link prediction and topological reconstruction. For the first time, it conducts a cross-disciplinary benchmark of thirteen unsupervised hyperbolic embedding approaches—drawn from machine learning, network science, and algorithms—within a unified experimental framework, encompassing maximum likelihood estimation, representation learning, and hybrid paradigms. The results reveal that performance differences stem primarily from the embedding paradigm rather than disciplinary origin, with maximum likelihood and representation learning methods generally outperforming others. However, no single method universally excels across all network structures and tasks. This work provides practical guidance for method selection and clarifies the network contexts in which each approach is most effective.

Abstract

Hyperbolic embeddings provide compact geometric representations of complex networks in hyperbolic spaces, but systematic comparisons of methods developed in machine learning, network science, and algorithmics remain rare. We benchmark 13 unsupervised hyperbolic graph embedders under a unified protocol for link prediction and topology reconstruction on synthetic and empirical networks. The protocol captures both missing-link recovery and the preservation of local and global network structure. Maximum-likelihood and representation-learning-based approaches, including hybrid variants, achieve the strongest overall performance, although no method dominates across all tasks and structural regimes. Performance is more strongly associated with embedding paradigm than with disciplinary origin. We identify the network regimes in which different paradigms succeed or fail and provide practical guidance for method selection in downstream applications.

Problem

• hyperbolic embeddings
• link prediction
• topology reconstruction
• graph embedders
• network structure

Innovation

• hyperbolic embeddings
• link prediction
• topology reconstruction
• unsupervised graph embedding
• benchmarking