Self-Organizing Graphs — A Neural Network Perspective of Graph Layout

  • Bernd Meyer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1547)


The paper presents self-organizing graphs, a novel approach to graph layout based on a competitive learning algorithm. This method is an extension of self-organization strategies known from unsupervised neural networks, namely from Kohonen’s self-organizing map. Its main advantage is that it is very flexibly adaptable to arbitrary types of visualization spaces, for it is explicitly parameterized by a metric model of the layout space. Yet the method consumes comparatively little computational resources and does not need any heavy-duty preprocessing. Unlike with other stochastic layout algorithms, not even the costly repeated evaluation of an objective function is required. To our knowledge this is the first connectionist approach to graph layout. The paper presents applications to 2D-layout as well as to 3D-layout and to layout in arbitrary metric spaces, such as networks on spherical surfaces.


Competitive Learning Graph Layout Layout Area Kohonen Network Competitive Layer 
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.


  1. [1]
    J.A. Anderson and E. Rosenfeld, editors. Neurocomputing. MIT Press, Combridge /MA, 1988.Google Scholar
  2. [2]
    F.J. Brandenburg, editor. Graph Drawing GD’95. Springer, Passau, Germany, September 1995.Google Scholar
  3. [3]
    F.J. Brandenburg, M. Himsolt, and C. Rohrer. An experimental comparison of force-directed and randomized graph drawing algorithms. In [2], pages 76–87.Google Scholar
  4. [4]
    I.F. Cruz and J.P. Twarog. 3D graph drawing with simulated annealing. In [2], pages 162–165.Google Scholar
  5. [5]
    R. Davidson and D. Harel.Drawing graphs nicely using simulated annealing. ACM Transactions on Graphics, 15(4):301–331, October 1996.Google Scholar
  6. [6]
    G. DiBattista, P. Eades, R. Tamassia, and G. Tollis. Algorithms for drawing graphs: an annotated bibliography. Journal of Computational Geometry Theory and Applications, 4:235–282, 1994.MathSciNetGoogle Scholar
  7. [7]
    M. Dorigo, V. Maniezzo, and A. Colorni. The ant system: Optimization by a colony of cooperating agents. IEEE Transactions on Systems, Man, and Cybernetics, 26(1):29–41, 1996.CrossRefGoogle Scholar
  8. [8]
    P. Eades. A heuristic for graph drawing. Congressus Numerantium, 42:149–160, 1984.MathSciNetGoogle Scholar
  9. [9]
    P. Frasconi, M. Gori, and A. Sperduti. A general framework for adaptive processing of data structures. Technical Report 15/97, Universita di Firenze, Florence, 1997.Google Scholar
  10. [10]
    B. Fritzke. Some competitive learning methods. Unpublished manuscript., April 1997.
  11. [11]
    C. Goller and A. Küchler. Learning task-dependent distributed representations by backpropagation through structure. In International Conference on Neural Networks (ICNN-96), 1996.Google Scholar
  12. [12]
    G.J. Goodhill and T.J. Sejnowski. A unifying objective function for topographic mappings. Neural Computation, 9:1291–1303, 1997.CrossRefGoogle Scholar
  13. [13]
    S. Grossberg. Adaptive pattern classification and universal recoding: Parallel development and coding of neural feature detectors. Biological Cybernetics, 23:121–134, 1976.CrossRefMathSciNetzbMATHGoogle Scholar
  14. [14]
    S. Grossberg. How does the brain build a cognitive code? Psychological Review, 87:1–51, 1980.CrossRefGoogle Scholar
  15. [15]
    S. Grossberg. Competitive learning: from interactive activation to adaptive resonance. Cognitive Science, 11:23–63, 1987.CrossRefGoogle Scholar
  16. [16]
    J. Hertz, A. Krogh, and R.G. Palmer. Introduction to the Theory of Neural Computation. Addison-Wesley, Redwood City/CA, 1991.Google Scholar
  17. [17]
    D. Hubel and T. Wiesel. Receptive fields, binocular interaction and functional architecture in the cat’s visual cortex. Journal of Physiology, 160:173–181, 1962.Google Scholar
  18. [18]
    T. Kohonen. Self-organized formation of topologically correct feature maps. Biological Cybernetics, 43:59–69, 1982.zbMATHCrossRefMathSciNetGoogle Scholar
  19. [19]
    T. Kohonen. Self-Organization and Associative Memory. Springer, New York, 1989.Google Scholar
  20. [20]
    T. Kohonen.Self-Organizing Maps. Springer, New York, 1997.Google Scholar
  21. [21]
    C. Kosak, J. Marks, and S. Shieber. Automating the layout of network diagrams with specified visual organization. IEEE Transactions on Systems, Man, and Cybernetics, 24(2):440–454, 1994.CrossRefGoogle Scholar
  22. [22]
    S.P. Luttrell. A bayesian analysis of self-organizing maps. Neural Computation, 6:767–794, 1994.zbMATHCrossRefGoogle Scholar
  23. [23]
    B.D. Ripley. Pattern Recognition and Neural Networks. Cambridge University Press, Cambridge/MA, 1996.zbMATHGoogle Scholar
  24. [24]
    K. Sugiyama. A cognitive approach for graph drawing. Cybernetics and Systems: An International Journal, 18:447–488, 1987.CrossRefGoogle Scholar
  25. [25]
    R. Tamassia. Constraints in graph drawing algorithms. Constraints, An International Journal, 3:87–120, 1998.zbMATHCrossRefMathSciNetGoogle Scholar
  26. [26]
    C. von der Malsburg. Self-organization of orientation sensitive cells in the striate cortex. Kybernetik, 14:85–100, 1973.CrossRefGoogle Scholar
  27. [27]
    S. Wolfram. The Mathematica Book, Third Edition. Cambridge University Press, Cambridge/MA, 1996.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Bernd Meyer
    • 1
  1. 1.University of MunichMunichGermany

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