Hyperbolic graph embedding: A survey and an evaluation on anomaly detection

Hyperbolic geometry has recently emerged as a powerful alternative to Euclidean spaces for representing graph-structured data, particularly due to its ability to capture hierarchical and scale-free structures with low distortion. This paper presents a comprehensive survey of hyperbolic graph embedding methods, providing both a conceptual overview and a systematic taxonomy of existing approaches. Beyond a purely descriptive survey, our work is specifically designed to address key limitations of existing surveys by incorporating a unified and reproducible experimental perspective. Unlike prior surveys, which mainly focus on theoretical foundations, our work places a particular emphasis on anomaly detection in graphs as a unifying and practically relevant evaluation task. To this end, we combine theoretical analysis with a unified evaluation protocol and a practical and reproducible evaluation framework, including a publicly available open-source library that provides a common platform implementing the most representative hyperbolic embedding methods. Using this framework, we conduct extensive experiments on diverse real-world datasets to systematically assess the effectiveness of hyperbolic representations for anomaly detection and to compare them against Euclidean baselines.