FADE: Graph Drawing, Clustering, and Visual Abstraction

  • Aaron Quigley
  • Peter Eades
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1984)

Abstract

A fast algorithm(fade) for the 2D drawing, geometric clustering and multilevel viewing of large undirected graphs is presented. The algorithm is an extension of the Barnes-Hut hierarchical space decomposition method, which includes edges and multilevel visual abstraction. Compared to the original force directed algorithm, the time overhead is O(e + n log n) where n and e are the numbers of nodes and edges. The improvement is possible since the decomposition tree provides a systematic way to determine the degree of closeness between nodes without explicitly calculating the distance between each node. Different types of regular decomposition trees are introduced. The decomposition tree also represents a hierarchical clustering of the nodes, which improves in a graph theoretic sense as the graph drawing approaches a lower energy state. Finally, the decomposition tree provides a mechanism to view the hierarchical clustering on various levels of abstraction. Larger graphs can be represented more concisely, on a higher level of abstraction, with fewer graphics on screen.

References

  1. 1.
    Richard J. Anderson, Tree data structures and n-body simulation, SIAM J. Comput. 28 (1999), no. 6, 1923–1940.MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    J. Barnes and P. Hut, A hierarchical o(n log n) force-calculation algorithm, Nature 324 (1986), no. 4, 446–449.CrossRefGoogle Scholar
  3. 3.
    Francois Bertault, A force-directed algorithm that preserves edge crossing properties, Seventh International Symposium on Graph Drawing (Prague, Chezh Republic) (Jan Kratochvíl, ed.), Springer, September 1999, pp. 351–358.Google Scholar
  4. 4.
    G. Blellcoh and G. Narlikar, A practical comparison of n-body algorithms, Technical report, Wright Laboratory, 1991.Google Scholar
  5. 5.
    Peter Eades, A heuristic for graph drawing, Congresses Numerantium 42 (1984), 149–160.MathSciNetGoogle Scholar
  6. 6.
    G. Erhard, Advances in system analysis vol. 4, graphs as structural models: The application of graphs and multigraphs in cluster analysis, Vieweg, 1988.Google Scholar
  7. 7.
    Q.W. Feng., Algorithms for drawing clustered graphs, Ph.D. thesis, The University of Newcastle, Australia, 1997.Google Scholar
  8. 8.
    T. Fruchterman and E. Reingold, Graph drawing by force-directed placement, Software-Practice and Experience 21 (1991), no. 11, 1129–1164.CrossRefGoogle Scholar
  9. 9.
    Roberto Tamassia G. Di Battista, P. Eades and I. G. Tollis, Graph drawing, algorithms for the visualization of graphs, Prentice-Hall Inc., 1999.Google Scholar
  10. 10.
    R. Hadany and David Harel, A multi-scale method for drawing graphs nicely, 25th International Workshop on Graph-Theoretic Concepts in Computer Science, 1999.Google Scholar
  11. 11.
    David Harel and Yehuda Koren, A fast multi-scale method for drawing large graphs, Technical report, Dept. of Applied Mathematics and Computer Science, Weizmann Institute, Rehovot, Israel, November 1999.Google Scholar
  12. 12.
    J. Hartigan, Clustering algorithms, Wiley, 1975.Google Scholar
  13. 13.
    W. He and K. Marriott, Constrained graph layout, Symposium on Graph Drawing, GD’ 96 (Stephen North, ed.), vol. 1190 of Lecture notes in Computer Science, Springer, 1996, pp. 217–232.Google Scholar
  14. 14.
    L. Hernquist, Hierarchical n-body methods, Computational Physics Communications 48 (1988), 107–115.CrossRefGoogle Scholar
  15. 15.
    R. W. Hockney and P. M. Sloot, Computer simulations using particles, McGraw-Hill, 1981.Google Scholar
  16. 16.
    Mao Huang, On-line animated visualization of huge graphs, Ph.D. thesis, The University of Newcastle, Australia, 1999.Google Scholar
  17. 17.
    Maurice M. de Ruiter Ivan Herman, Guy Melançon and Maylis Delest, Latoura tree visualisation system, Seventh International Symposium on Graph Drawing (Prague, Chezh Republic) (Jan Kratochvíl, ed.), Springer, September 1999, pp. 392–399.Google Scholar
  18. 18.
    L. Greengard J. Carriert and V. Rokhlin, A fast adaptive multipole algorithm for particle simulations, SIAM Journal on Scientific Computing 9 (1988), no. 4, 669–686.MATHCrossRefGoogle Scholar
  19. 19.
    Arunabha Sen Jubin Edachery and Franz J. Brandenburg, Graph clustering using distance-k cliques, 7th International Symposium on Graph Drawing, GD’ 99 (Jan Kratochvíl, ed.), vol. 1731 of Lecture notes in Computer Science, Springer, 1999, pp. 98–106.Google Scholar
  20. 20.
    P. Eades et al K. Misue, Layout adjustment and the mental map, Journal of Visual Languages and Computing (1995), 183–210.Google Scholar
  21. 21.
    George Karypis and Vipin Kumar, A fast and high quality multilevel scheme for partitioning irregular graphs, SIAM Journal on Scientific Computing (1998).Google Scholar
  22. 22.
    —, A parallel algorithm for multilevel graph partitioning and sparse matrix ordering, Journal of Parallel and Distributed Computing (1998).Google Scholar
  23. 23.
    B. W. Kernighan and S. Lin, An efficient heuristic procedure for partitioning graphs, The Bell System Techinical Journal (1970).Google Scholar
  24. 24.
    M. Lorr, Cluster analysis for social scientists, Jossey-Bass Ltd., 1987.Google Scholar
  25. 25.
    Susanne Pfalzner and Paul Gibbon, Many-body tree methods in physics, Cambridge University Press, 1996.Google Scholar
  26. 26.
    R. Cohen Q. W. Feng and P. Eades, How to draw a planer clustered graph, CO-COON, vol. 959, Lecture notes in Computer Science, Springer, 1995, pp. 21–31.Google Scholar
  27. 27.
    Reinhard Sablowski and Arne Frick, Automatic graph clustering (system demonstration), Symposium on Graph Drawing, GD’ 96 (Stephen North, ed.), vol. 1190 of Lecture notes in Computer Science, Springer, 1996, pp. 395–400.Google Scholar
  28. 28.
    Manojit Sarkar and Marc Brown, Graphical fisheye views of graphs, ACM SIGCHI’ 92 Conference on Human Factors in Computing Systems, March 1992.Google Scholar
  29. 29.
    Horst Simon and Shang-Hua Teng, How good is recursive bisection, Nasa-publication, Ames Research Center NASA, June 1993.Google Scholar
  30. 30.
    H. Spath, Cluster analysis algorithms for data reduction and classification of objects, Horwood, 1980.Google Scholar
  31. 31.
    K. Sugiyama and K. Misue, A simple and unified method for drawing graphs: Magnetic-spring algorithm, Proceedings of Graph Drawing, GD’ 94 (Roberto Tamassia and Ioannis Tollis, eds.), vol. 894 of Lecture Notes in Computer Science, Springer, 1995, pp. 364–375.Google Scholar
  32. 32.
    S. Teng, Points, spheres, and separators: A unified geometric approach to graph partitioning, Ph.D. thesis, School of Computer Science, Carnegir Mellon University, 1991.Google Scholar
  33. 33.
    Edward R. Tufte, The visual display of quatitative information, Graphics Press, 1983.Google Scholar
  34. 34.
    —, Envisioning information, Graphics Press, 1990.Google Scholar
  35. 35.
    —, Visual explanations, Graphics Press, 1997.Google Scholar
  36. 36.
    Daniel Tunkelang, Jiggle: Java interactive general graph layout environment, Sixth International Symposium on Graph Drawing (McGill University, Canada) (Sue Whitesides, ed.), Springer, August 1998.Google Scholar
  37. 37.
    Andrej Mrvar Vladimir Batagelj and Matjaz Zaveršnik, Partitioning approach to visualization of large graphs, 7th International Symposium on Graph Drawing, GD’ 99 (Jan Kratochvíl, ed.), vol. 1731 of Lecture notes in Computer Science, Springer, 1999, pp. 90–97.Google Scholar
  38. 38.
    Jiong Yang Wei Wang and Richard Muntz, Sting: A statistical information grid approach to spatial data mining, 23rd International Conference on Very Large Data Bases(VLDB), IEEE, 1997, pp. 186–195.Google Scholar
  39. 39.
    —, Sting+: An approach to active spatial data mining, IEEE, 1999, pp. 116–125.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Aaron Quigley
    • 1
  • Peter Eades
    • 1
  1. 1.Department of Computer Science and Software EngineeringUniv. of NewcastleCallaghanAustralia

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