Hierarchical Layouts of Directed Graphs in Three Dimensions

  • Seok-Hee Hong
  • Nikola S. Nikolov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3843)


We introduce a new graph drawing convention for 3D hierarchical drawings of directed graphs. The vertex set is partitioned into layers of vertices drawn in parallel planes. The vertex set is further partitioned into k ≥ 2 subsets, called walls. The layout consists of a set of parallel walls which are perpendicular to the set of parallel planes of the layers. We also outline a method for computing such layouts and introduce four alternative algorithms for partitioning the vertex set into walls which address different aesthetic requirements.


  1. 1.
    Brandes, U., Köpf, B.: Fast and simple horizontal coordinate assignment. In: Mutzel, P., Jünger, M., Leipert, S. (eds.) GD 2001. LNCS, vol. 2265, pp. 31–44. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  2. 2.
    Di Battista, G., Eades, P., Tamassia, R., Tollis, I.G.: Graph Drawing. Prentice-Hall, Englewood Cliffs (1999)MATHGoogle Scholar
  3. 3.
    Di Battista, G., Garg, A., Liotta, G., Tamassia, R., Tassinari, E., Vargiu, F.: An experimental comparison of four graph drawing algorithms. Computational Geometry: Theory and Applications 7, 303–316 (1997)MATHMathSciNetGoogle Scholar
  4. 4.
    Eades, P., Sugiyama, K.: How to draw a directed graph. Journal of Information Processing 13(4), 424–437 (1990)MATHGoogle Scholar
  5. 5.
    Garg, A., Tamassia, R.: GIOTTO: A system for visualizing hierarchical structures in 3D. In: North, S.C. (ed.) GD 1996. LNCS, vol. 1190, pp. 193–200. Springer, Heidelberg (1997)Google Scholar
  6. 6.
    Hong, S.-H., Nikolov, N.S.: Layered drawings of directed graphs in three dimensions. In: Hong, S.-H. (ed.) Information Visualisation 2005: Asia-Pacific Symposium on Information Visualisation (APVIS 2005), vol. 45, pp. 69–74. CRPIT (2005)Google Scholar
  7. 7.
    Nikolov, N.S., Tarassov, A.: Graph layering by promotion of nodes. In: Special issue of Discrete Applied Mathematics associated with the IV ALIO/EURO Workshop on Applied Combinatorial Optimization (to appear)Google Scholar
  8. 8.
    Ostry, D.: Some three-dimensional graph drawing algorithms. Master’s thesis, University of Newcastle (1996)Google Scholar
  9. 9.
    Sugiyama, K., Tagawa, S., Toda, M.: Methods for visual understanding of hierarchical system structures. IEEE Transaction on Systems, Man, and Cybernetics 11(2), 109–125 (1981)CrossRefMathSciNetGoogle Scholar
  10. 10.
    Ware, C., Franck, G.: Viewing a graph in a virtual reality display is three times as good as a 2D diagram. In: IEEE Conference on Visual Languages, pp. 182–183 (1994)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Seok-Hee Hong
    • 1
    • 2
  • Nikola S. Nikolov
    • 1
    • 3
  1. 1.IMAGEN ProgramNational ICT Australia Ltd. 
  2. 2.School of ITUniversity of SydneyAustralia
  3. 3.Department of CSISUniversity of LimerickLimerickRepublic of Ireland

Personalised recommendations