Maintaining the Mental Map for Circular Drawings

  • Michael Kaufmann
  • Roland Wiese
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2528)

Abstract

In this paper we present new ideas to extend the framework for circular drawing of networks bySix and Tollis [15] bysome new concepts which makes the framework suitable for user interaction. The original approach displays each biconnected component in a circular way, and the blocktree of the graph as a tree drawn radially [9]. We introduce the concept of hicircular drawings, a hierarchical extension of the mentioned framework replacing the circles of single vertices bycircles of circular or star-like structures. This concept is inspired bythe works of Brandenburg on graph clustering, and the recursive concepts of series-parallel graphs, PQ- resp. SPQR-trees.

References

  1. 1.
    Booth, K.S. and Lueker G.S., Testing for the consecutive ones property, intervals graphs and graph planarity testing using PQ-tree algorithms, J. Comput. System Sci.13, pp. 335–379, 1976.MATHMathSciNetGoogle Scholar
  2. 2.
    Brandenburg F., Graph Clustering 1: Cycles of Cliques, Proc. GD’97, LNCS 1353, Springer, pp. 158–168, 1998.Google Scholar
  3. 3.
    Branke J., Dynamic Graph Drawing, in Kaufmann/Wagner (Eds.) Drawing Graphs: Methods and Models, LNCS 2025, Springer, pp. 228–246CrossRefGoogle Scholar
  4. 4.
    Brockenauer R. and S. Cornelsen, Drawing Clusters and Hierarchies, in Kaufmann/ Wagner (Eds.) Drawing Graphs: Methods and Models, LNCS 2025, Springer, pp. 193–227, 2001.Google Scholar
  5. 5.
    Di Battista, G., Eades P., Tamassia R. and I. G. Tollis, Graph Drawing: Algorithms for the Visualization of Graphs, Prentice Hall, 1999.Google Scholar
  6. 6.
    Di Battista G., and Tamassia R., On-line graph algorithms with SPQR-trees, Proc. ICALP 1990, LNCS 442, Springer, pp. 598–611, 1990.Google Scholar
  7. 7.
    Dogrusöz U., B. Madden and P. Madden, Circular Layout in the Graph Layout Toolkit, Proc. GD’96, LNCS 1190, Springer, pp. 92–100, 1997.Google Scholar
  8. 8.
    Duncan Ch., Goodrich M., and Kobourov St., Planarity-Preserving Clustering and Embedding of Large Graphs, Proc. GD’99, LNCS 1731, Springer, pp. 186–196, 2000.Google Scholar
  9. 9.
    Eades P., Drawing Free Trees, Bulletin of the Institute for Combinatorics and its Applications, 5, pp. 10–36, 1992.MATHMathSciNetGoogle Scholar
  10. 10.
    Edachery, J., Sen A., Brandenburg F., Graph Clustering Using Distance-k Cliques, Proc. GD’99, LNCS 1731, Springer, pp. 98–106, 2000..Google Scholar
  11. 11.
    Kar G., B. Madden and R. Gilbert, Heuristic Layout Algorithms for Network Presentation Services, IEEE Network, 11, pp. 29–36, 1988.CrossRefGoogle Scholar
  12. 12.
    Krebs V., Visualizing Human Networks, Release 1.0: Esther Dyson’s Monthly Report, pp. 1–25, 1996.Google Scholar
  13. 13.
    Lengauer T., Combinatorial Algorithms for Integrated Circuit Layout, Wiley-Teubner, 1990.Google Scholar
  14. 14.
    Six, J.M. and I.G. Tollis, Circular Drawings of Biconnected Graphs, Proc. Alenex’99, LNCS 1619, Springer, pp. 57–73, 1999.Google Scholar
  15. 15.
    Six, J.M. and I.G. Tollis, A Framework for Circular Drawings of Networks, Proc.GD’99, LNCS 1731, Springer, pp. 107–116, 2000.Google Scholar
  16. 16.
    Six, J.M., Ph.D. Thesis, Universityof Texas at Dallas, 2000.Google Scholar
  17. 17.
    Sugiyama K., S. Tagawa and M. Toda. Methods for Visual Understanding of Hierarchical System Structures, IEEE Transactions on Systems, Man and Cybernetics, 11(2), pp. 109–125, 1MathSciNetGoogle Scholar
  18. 18.
    Sugiyama K., K. Misue. Visualisation of structural information: Automatic drawing of compound digraphs, IEEE Transactions on Systems, Man and Cybernetics, 21(4), pp. 876–892, 1991.MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Michael Kaufmann
    • 1
  • Roland Wiese
    • 1
    • 2
  1. 1.Wilhelm-Schickard-Institut für InformatikUniversität TübingenTübingen
  2. 2.yWorks GmbHTübingen

Personalised recommendations