Multilevel Drawings of Clustered Graphs

  • Fabrizio Frati
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7434)

Abstract

The cluster adjacency graph of a flat clustered graph C(G,T) is the graph A whose vertices are the clusters in T and whose edges connect clusters containing vertices that are adjacent in G. A multilevel drawing of a clustered graph C consists of a straight-line c-planar drawing of C in which the clusters are drawn as convex regions and of a straight-line planar drawing of A such that each vertex a ∈ A is drawn in the cluster corresponding to a and such that no edge (a 1,a 2) ∈ A intersects any cluster different from a 1 and a 2. In this paper, we show that every c-planar flat clustered graph admits a multilevel drawing.

Keywords

Extension Region Common Neighbor Internal Vertex Outer Face Convex Region 
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.

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References

  1. 1.
    Angelini, P., Frati, F., Kaufmann, M.: Straight-line rectangular drawings of clustered graphs. Discrete & Computational Geometry 45(1), 88–140 (2011)MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Di Battista, G., Drovandi, G., Frati, F.: How to draw a clustered tree. J. Discrete Algorithms 7(4), 479–499 (2009)MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Di Battista, G., Frati, F.: Efficient c-planarity testing for embedded flat clustered graphs with small faces. J. Graph Alg. Appl. 13(3), 349–378 (2009)MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Eades, P., Feng, Q.: Multilevel Visualization of Clustered Graphs. In: DiBattista, G. (ed.) GD 1997. LNCS, vol. 1353, pp. 101–112. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  5. 5.
    Eades, P., Feng, Q., Lin, X., Nagamochi, H.: Straight-line drawing algorithms for hierarchical graphs and clustered graphs. Algorithmica 44(1), 1–32 (2006)MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Eades, P., Feng, Q., Nagamochi, H.: Drawing clustered graphs on an orthogonal grid. J. Graph Alg. Appl. 3(4), 3–29 (1999)MathSciNetMATHGoogle Scholar
  7. 7.
    Feng, Q.: Algorithms for drawing clustered graphs. Ph. D. thesis. The University of Newcastle, Australia (1997)Google Scholar
  8. 8.
    Feng, Q., Cohen, R.F., Eades, P.: How to Draw a Planar Clustered Graph. In: Li, M., Du, D.-Z. (eds.) COCOON 1995. LNCS, vol. 959, pp. 21–30. Springer, Heidelberg (1995)CrossRefGoogle Scholar
  9. 9.
    Feng, Q., Cohen, R.F., Eades, P.: Planarity for Clustered Graphs. In: Spirakis, P.G. (ed.) ESA 1995. LNCS, vol. 979, pp. 213–226. Springer, Heidelberg (1995)CrossRefGoogle Scholar
  10. 10.
    Jelínková, E., Kára, J., Kratochvíl, J., Pergel, M., Suchý, O., Vyskocil, T.: Clustered planarity: Small clusters in cycles and Eulerian graphs. J. Graph Alg. Appl. 13(3), 379–422 (2009)MATHCrossRefGoogle Scholar
  11. 11.
    Jünger, M., Leipert, S., Percan, M.: Triangulating clustered graphs. Technical report. Zentrum für Angewandte Informatik Köln (2002)Google Scholar
  12. 12.
    Nagamochi, H., Kuroya, K.: Drawing c-planar biconnected clustered graphs. Discr. Appl. Math. 155(9), 1155–1174 (2007)MathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    Schaeffer, S.E.: Graph clustering. Computer Science Review 1(1), 27–64 (2007)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Tutte, W.T.: How to draw a graph. Proc. London Math. Soc. 13(52), 743–768 (1963)MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Fabrizio Frati
    • 1
  1. 1.School of Information TechnologiesThe University of SydneyAustralia

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