Hyperbolic Embedders Benchmarked for Graph Link Prediction

Hyperbolic embeddings offer a compact and geometric way to represent complex networks within hyperbolic spaces. Despite their potential, a comprehensive comparison of different methods developed across machine learning, network science, and algorithmics has been lacking. This research addresses that gap by benchmarking 13 unsupervised hyperbolic graph embedders. The evaluation uses a unified protocol to assess their effectiveness in both link prediction (recovering missing connections) and topology reconstruction (preserving local and global network structures) across synthetic and empirical networks. The findings indicate that approaches based on maximum-likelihood and representation learning, including hybrid variants, generally deliver the strongest overall performance. However, the study also reveals that no single method is universally superior across all tasks and structural network regimes. Instead, performance is more closely linked to the underlying embedding paradigm rather than its disciplinary origin. The research identifies specific network conditions under which different paradigms succeed or fail, providing practical guidance for professionals on selecting the most appropriate hyperbolic embedding method for their particular downstream applications.