@inproceedings{NaamaEtAl:SDM26,
  author	= {Naama, Saloua and Salamatian, Kave and Crovella, Mark},
  title		= {Geometric Hyperbolic Embedding of Metric Graphs Through Graph Decomposition},
  year		= {2026},
  booktitle	= {Proceedings of SIAM International Conference on Data Mining},
  month		= nov,
  URL		= TBD,
  doi		= TBD
  abstract	= {In recent years, hyperbolic embeddings of graphs have emerged as a critical area of research, with wide-ranging applications across geometry, machine learning, and graph mining. These embeddings enable low-distortion, compact representations of complex graph structures. While numerous combinatorial and optimization-based approaches have been developed, they often suffer from high computational cost and numerical instability. In this paper, we propose a novel, geometry-inspired method for hyperbolic graph embedding. Our formulation introduces a fundamentally different perspective from existing approaches, avoiding the use of artificial or auxiliary vertices that may alter the intrinsic structural properties of the graph. Central to our approach is the matching of the geometry of the hyperbolic space, with the structural properties of the graph. We leverage this matching in the two major contributions of the paper, namely a reformulation of the hyperbolic embedding as an euclidean embedding with a different metric space, and the use of clique separator decomposition, which allows for efficient structural analysis and significantly reduces the complexity of the embedding process, while simultaneously enhancing embedding quality. We validate our developed methods through comprehensive experiments on both synthetic and real-world datasets, demonstrating its effectiveness and advantages over prior techniques. Overall, our findings illustrate that geometric insights -- particularly those grounded in hyperbolic geometry -- can offer powerful tools for understanding, embedding, and visualizing complex graph structures.}
}