A Framework for User-Grouped Circular Drawings

  • Janet M. Six
  • Ioannis (Yanni) G. Tollis
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2912)


In this paper we introduce a framework for producing circular drawings in which the groupings are user-defined. These types of drawings can be used in applications for telecommunications, computer networks, social network analysis, project management, and more. This fast approach produces drawings in which the user-defined groupings are highly visible, each group is laid out with a low number of edge crossings, and the number of crossings between intra-group and inter-group edges is low.


  1. 1.
    Bernard, M.A.: On the Automated Drawing of Graphs. In: Proc. 3rd Caribbean Conf. on Combinatorics and Computing, pp. 43–55 (1994)Google Scholar
  2. 2.
    Brandenburg, F.: Graph Clustering 1: Cycles of Cliques. In: DiBattista, G. (ed.) GD 1997. LNCS, vol. 1353, pp. 158–168. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  3. 3.
    Di Battista, G., Eades, P., Tamassia, R., Tollis, I.G.: Graph Drawing: Algorithms for the Visualization of Graphs. Prentice-Hall, Englewood Cliffs (1999)MATHGoogle Scholar
  4. 4.
    Doğrusöz, U., Madden, B., Madden, P.: Circular Layout in the Graph Layout Toolkit. In: North, S.C. (ed.) GD 1996. LNCS, vol. 1190, pp. 92–100. Springer, Heidelberg (1997)Google Scholar
  5. 5.
    Eades, P.: A Heuristic for Graph Drawing, Congr. Numer., 42, 149–160 (1984)Google Scholar
  6. 6.
    Eades, P., Feng, Q., Lin, X.: Straight-Line Drawing Algorithms for Hierarchical Graphs and Clustered Graphs. In: North, S.C. (ed.) GD 1996. LNCS, vol. 1190, pp. 113–128. Springer, Heidelberg (1997)Google Scholar
  7. 7.
    Eades, P., Feng, Q.W.: Multilevel Visualization of Clustered Graphs. In: North, S.C. (ed.) GD 1996. LNCS, vol. 1190, pp. 101–112. Springer, Heidelberg (1997)Google Scholar
  8. 8.
    Eades, P., Feng, Q.W., Nagamochi, H.: Drawing Clustered Graphs on an Orthogonal Grid. Jrnl. of Graph Algorithms and Applications, 3–29 (1999)Google Scholar
  9. 9.
    Esposito, C.: Graph Graphics: Theory and Practice. Comput. Math. Appl. 15(4), 247–253 (1988)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Garey, M., Johnson, D.: Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, San Francisco (1979)MATHGoogle Scholar
  11. 11.
    Halliday, D., Resnick, R.: Fundamentals of Physics, 3rd edn. Extended. Wiley, New York (1988)Google Scholar
  12. 12.
    Huang, M.L., Eades, P.: A Fully Animated Interactive System for Clustering and Navigating Huge Graphs. In: Whitesides, S.H. (ed.) GD 1998. LNCS, vol. 1547, pp. 107–116. Springer, Heidelberg (1999)Google Scholar
  13. 13.
    Kar, G., Madden, B., Gilbert, R.: Heuristic Layout Algorithms for Network Presentation Services. IEEE Network 11, 29–36 (1988)CrossRefGoogle Scholar
  14. 14.
    Kaufmann, M., Wiese, R.: Maintaining the Mental Map for Circular Drawings. In: Goodrich, M.T., Kobourov, S.G. (eds.) GD 2002. LNCS, vol. 2528, pp. 12–22. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  15. 15.
    Kershenbaum, A.: Telecommunications Network Design Algorithms. McGraw-Hill, New York (1993)MATHGoogle Scholar
  16. 16.
    Krebs, V.: Visualizing Human Networks, Release 1.0: Esther Dyson’s Monthly Report, pp. 1–25, February 12 (1996)Google Scholar
  17. 17.
    Masuda, S., Kashiwabara, T., Nakajima, K., Fujisawa, T.: On the NP-Completeness of a Computer Network Layout Problem. In: Proc. IEEE 1987 International Symposium on Circuits and Systems, Philadelphia, PA, pp. 292–295 (1987)Google Scholar
  18. 18.
    Mitchell, S.: Linear Algorithms to Recognize Outerplanar and Maximal Outerplanar Graphs. Information Processing Letters 9(5), 229–232 (1979)MATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Purchase, H.: Which Aesthetic has the Greatest Effect on Human Understanding. In: DiBattista, G. (ed.) GD 1997. LNCS, vol. 1353, pp. 248–261. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  20. 20.
    Six, J.M.(Urquhart): Vistool: A Tool For Visualizing Graphs, Ph.D. Thesis, The University of Texas at Dallas (2000)Google Scholar
  21. 21.
    Six, J.M., Tollis, I.G.: Circular Drawings of Biconnected Graphs. In: Goodrich, M.T., McGeoch, C.C. (eds.) ALENEX 1999. LNCS, vol. 1619, pp. 57–73. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  22. 22.
    Six, J.M., Tollis, I.G.: Circular Drawings of Telecommunication Networks. In: Fotiadis, D.I., Nikolopoulos, S.D. (eds.) Advances in Informatics, Selected Papers from HCI 1999, pp. 313–323. World Scientific, Singapore (2000)Google Scholar
  23. 23.
    Six, J.M., Tollis, I.G.: Effective Graph Visualization Via Node Grouping. In: Zhang, K. (ed.) Software Visualization: From Theory to Practice. The Kluwer Intl. Series in Engineering and Computer Science, vol. 734, Kluwer Academic Publishers, Dordrecht (2003)Google Scholar
  24. 24.
    Six, J.M., Tollis, I.G.: A Framework for Circular Drawings of Networks. In: Kratochvíl, J. (ed.) GD 1999. LNCS, vol. 1731, pp. 107–116. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  25. 25.
    Tollis, G., Xia, C.: Drawing Telecommunication Networks. In: Tamassia, R., Tollis, I.G. (eds.) GD 1994. LNCS, vol. 894, pp. 206–217. Springer, Heidelberg (1994)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Janet M. Six
    • 1
  • Ioannis (Yanni) G. Tollis
    • 2
    • 3
  1. 1.Lone Star Interface DesignWylieUSA
  2. 2.Department of Computer ScienceUniversity of CreteHeraklionGreece
  3. 3.Institute of Computer ScienceFoundation for Research and Technology Hellas-FORTHHeraklion, CreteGreece

Personalised recommendations