More Flexible Radial Layout

  • Ulrik Brandes
  • Christian Pich
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5849)


We describe an algorithm for radial layout of undirected graphs, in which nodes are constrained to the circumferences of a set of concentric circles around the origin. Such constraints frequently occur in the layout of social or policy networks, when structural centrality is mapped to geometric centrality, or when the primary intention of the layout is the display of the vicinity of a distinguished node. We extend stress majorization by a weighting scheme which imposes radial constraints on the layout but also tries to preserve as much information about the graph structure as possible.


Multidimensional Scaling Layout Problem Constraint Stress Graph Drawing Minimum Travel Time 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Bachmaier, C., Brandenburg, F.J., Forster, M.: Radial level planarity testing and embedding in linear time. Journal of Graph Algorithms and Applications 9(1), 53–97 (2005)zbMATHMathSciNetGoogle Scholar
  2. 2.
    Borg, I., Groenen, P.: Modern Multidimensional Scaling. Springer, Heidelberg (2005)zbMATHGoogle Scholar
  3. 3.
    Borg, I., Lingoes, J.: A model and algorithm for multidimensional scaling with external constraints on the distances. Psychometrika 45(1), 25–38 (1980)zbMATHCrossRefGoogle Scholar
  4. 4.
    Brandes, U., Kenis, P., Wagner, D.: Communicating centrality in policy network drawings. IEEE Transactions on Visualization and Computer Graphics 9(2), 241–253 (2003)CrossRefGoogle Scholar
  5. 5.
    Brandes, U., Pich, C.: An experimental study on distance-based graph drawing. In: Tollis, I.G., Patrignani, M. (eds.) GD 2008. LNCS, vol. 5417, pp. 218–229. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  6. 6.
  7. 7.
    Cox, T.F., Cox, M.A.A.: Multidimensional Scaling. CRC/Chapman and Hall, Boca Raton (2001)zbMATHGoogle Scholar
  8. 8.
    de Leeuw, J.: Applications of convex analysis to multidimensional scaling. In: Barra, J.R., Brodeau, F., Romier, G., van Cutsem, B. (eds.) Recent Developments in Statistics, pp. 133–145. North-Holland, Amsterdam (1977)Google Scholar
  9. 9.
    de Leeuw, J.: Convergence of the majorization method for multidimensional scaling. Journal of Classification 5(2), 163–180 (1988)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Dwyer, T., Marriott, K., Wybrow, M.: Topology preserving constrained graph layout. In: Tollis, I.G., Patrignani, M. (eds.) GD 2008. LNCS, vol. 5417, pp. 230–241. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  11. 11.
    Gansner, E.R., Hu, Y.: Efficient node overlap removal using a proximity stress model. In: Tollis, I.G., Patrignani, M. (eds.) GD 2008. LNCS, vol. 5417, pp. 206–217. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  12. 12.
    Gansner, E.R., Koren, Y., North, S.: Graph drawing by stress majorization. In: Pach, J. (ed.) GD 2004. LNCS, vol. 3383, pp. 239–250. Springer, Heidelberg (2005)Google Scholar
  13. 13.
    Heiser, W.J., Meulman, J.: Constrained multidimensional scaling, including confirmation. Applied Psychological Measurement 7(4), 381–404 (1983)CrossRefGoogle Scholar
  14. 14.
    Hong, S.-H., Merrick, D., do Nascimiento, H.A.D.: The metro map layout problem. In: Proceedings of the 2004 Australasian symposium on Information Visualisation. ACM International Conference Proceeding Series, pp. 91–100 (2004)Google Scholar
  15. 15.
    Kamada, T., Kawai, S.: An algorithm for drawing general undirected graphs. Information Processing Letters 31, 7–15 (1989)zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Koren, Y., Çivril, A.: The binary stress model for graph drawing. In: Tollis, I.G., Patrignani, M. (eds.) GD 2008. LNCS, vol. 5417, pp. 193–205. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  17. 17.
    McGee, V.E.: The multidimensional scaling of “elastic” distances. The British Journal of Mathematical and Statistical Psychology 19, 181–196 (1966)Google Scholar
  18. 18.
    Northway, M.L.: A method for depicting social relationships obtained by sociometric testing. Sociometrics 3, 144–150 (1940)CrossRefGoogle Scholar
  19. 19.
    Wills, G.J.: NicheWorks – interactive visualization of very large graphs. In: DiBattista, G. (ed.) GD 1997. LNCS, vol. 1353, pp. 403–414. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  20. 20.
    Yee, K.-P., Fisher, D., Dhamija, R., Hearst, M.: Animated exploration of dynamic graphs with radial layout. In: Proc. InfoVis, pp. 43–50 (2001)Google Scholar
  21. 21.
    Zachary, W.W.: An information flow model for conflict and fission in small groups. Journal of Anthropological Research 33, 452–473 (1977)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Ulrik Brandes
    • 1
  • Christian Pich
    • 2
  1. 1.Department of Computer & Information ScienceUniversity of Konstanz 
  2. 2.Chair of Systems DesignETH Zürich 

Personalised recommendations