2026-07-29T11:23:47Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:13794 2024-03-06T10:52:58Z ddc:004 open_access

Force-Directed Embedding of Scale-Free Networks in the Hyperbolic Plane Bläsius, Thomas Friedrich, Tobias Katzmann, Maximilian force-directed drawing algorithms spring embedding hyperbolic space Force-directed drawing algorithms are the most commonly used approach to visualize networks. While they are usually very robust, the performance of Euclidean spring embedders decreases if the graph exhibits the high level of heterogeneity that typically occurs in scale-free real-world networks. As heterogeneity naturally emerges from hyperbolic geometry (in fact, scale-free networks are often perceived to have an underlying hyperbolic geometry), it is natural to embed them into the hyperbolic plane instead. Previous techniques that produce hyperbolic embeddings usually make assumptions about the given network, which (if not met) impairs the quality of the embedding. It is still an open problem to adapt force-directed embedding algorithms to make use of the heterogeneity of the hyperbolic plane, while also preserving their robustness. We identify fundamental differences between the behavior of spring embedders in Euclidean and hyperbolic space, and adapt the technique to take advantage of the heterogeneity of the hyperbolic plane. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Thomas Bläsius and Tobias Friedrich and Maximilian Katzmann 2021 Is Part Of LIPIcs, Volume 190, 19th International Symposium on Experimental Algorithms (SEA 2021) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.SEA.2021.22 urn:nbn:de:0030-drops-137944 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2021.22 eng https://creativecommons.org/licenses/by/4.0/legalcode