Non-Euclidean spring embedders

Stephen G. Kobourov, Kevin Wampler

Research output: Contribution to journalArticlepeer-review

29 Scopus citations


We present a conceptually simple approach to generalizing force-directed methods for graph layout from Euclidean geometry to Riemannian geometries. Unlike previous work on non-Euclidean force-directed methods, ours is not limited to special classes of graphs, but can be applied to arbitrary graphs. The method relies on extending the Euclidean notions of distance, angle, and force-interactions to smooth non-Euclidean geometries via projections to and from appropriately chosen tangent spaces. In particular, we formally describe the calculations needed to extend such algorithms to hyperbolic and spherical geometries. We also study the theoretical and practical considerations that arise when working with non-Euclidean geometries.

Original languageEnglish (US)
Pages (from-to)757-767
Number of pages11
JournalIEEE Transactions on Visualization and Computer Graphics
Issue number6
StatePublished - Nov 2005


  • Force-directed algorithms
  • Graph drawing
  • Hyperbolic space
  • Information visualization
  • Non-Euclidean geometry
  • Spherical space
  • Spring embedders

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Computer Vision and Pattern Recognition
  • Computer Graphics and Computer-Aided Design


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