Simplification of Networks by Edge Pruning

  • Fang Zhou
  • Sébastien Mahler
  • Hannu Toivonen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7250)


We propose a novel problem to simplify weighted graphs by pruning least important edges from them. Simplified graphs can be used to improve visualization of a network, to extract its main structure, or as a pre-processing step for other data mining algorithms.

We define a graph connectivity function based on the best paths between all pairs of nodes. Given the number of edges to be pruned, the problem is then to select a subset of edges that best maintains the overall graph connectivity. Our model is applicable to a wide range of settings, including probabilistic graphs, flow graphs and distance graphs, since the path quality function that is used to find best paths can be defined by the user. We analyze the problem, and give lower bounds for the effect of individual edge removal in the case where the path quality function has a natural recursive property. We then propose a range of algorithms and report on experimental results on real networks derived from public biological databases.

The results show that a large fraction of edges can be removed quite fast and with minimal effect on the overall graph connectivity. A rough semantic analysis of the removed edges indicates that few important edges were removed, and that the proposed approach could be a valuable tool in aiding users to view or explore weighted graphs.


Edge Weight Weighted Graph Brute Force Combinational Approach Good Path 
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.
    Zhou, F., Mahler, S., Toivonen, H.: Network Simplification with Minimal Loss of Connectivity. In: The 10th IEEE International Conference on Data Mining (ICDM), Sydney, Australia, pp. 659–668 (2010)Google Scholar
  2. 2.
    Dubitzky, W., Kötter, T., Schmidt, O., Berthold, M.R.: Towards Creative Information Exploration Based on Koestler’s Concept of Bisociation. In: Berthold, M.R. (ed.) Bisociative Knowledge Discovery. LNCS (LNAI), vol. 7250, pp. 11–32. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  3. 3.
    Zhou, F., Mahler, S., Toivonen, H.: Review of BisoNet Abstraction Techniques. In: Berthold, M.R. (ed.) Bisociative Knowledge Discovery. LNCS (LNAI), vol. 7250, pp. 166–178. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  4. 4.
    Toivonen, H., Mahler, S., Zhou, F.: A Framework for Path-Oriented Network Simplification. In: Cohen, P.R., Adams, N.M., Berthold, M.R. (eds.) IDA 2010. LNCS, vol. 6065, pp. 220–231. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  5. 5.
    Sevon, P., Eronen, L., Hintsanen, P., Kulovesi, K., Toivonen, H.: Link Discovery in Graphs Derived from Biological Databases. In: Leser, U., Naumann, F., Eckman, B. (eds.) DILS 2006. LNCS (LNBI), vol. 4075, pp. 35–49. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  6. 6.
    Kruskal Jr., J.: On the shortest spanning subtree of a graph and the traveling salesman problem. Proceedings of the American Mathematical society 7(1), 48–50 (1956)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Biedl, T.C., Brejová, B., Vinař, T.: Simplifying Flow Networks. In: Nielsen, M., Rovan, B. (eds.) MFCS 2000. LNCS, vol. 1893, pp. 192–201. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  8. 8.
    Misiołek, E., Chen, D.Z.: Efficient Algorithms for Simplifying Flow Networks. In: Wang, L. (ed.) COCOON 2005. LNCS, vol. 3595, pp. 737–746. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  9. 9.
    Schvaneveldt, R., Durso, F., Dearholt, D.: Network structures in proximity data. In: The Psychology of Learning and Motivation: Advances in Research and Theory, vol. 24, pp. 249–284. Academic Press, New York (1989)Google Scholar
  10. 10.
    Quirin, A., Cordon, O., Santamaria, J., Vargas-Quesada, B., Moya-Anegon, F.: A new variant of the Pathfinder algorithm to generate large visual science maps in cubic time. Information Processing and Management 44, 1611–1623 (2008)CrossRefGoogle Scholar
  11. 11.
    Hauguel, S., Zhai, C., Han, J.: Parallel PathFinder Algorithms for Mining Structures from Graphs. In: Proceedings of the 2009 Ninth IEEE International Conference on Data Mining, ICDM 2009, pp. 812–817. IEEE Computer Society, Washington, DC (2009)CrossRefGoogle Scholar
  12. 12.
    Toussaint, G.T.: The Relative Neighbourhood Graph of a Finite Planar Set. Pattern Recognition 12(4), 261–268 (1980)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Osipov, V., Sanders, P., Singler, J.: The Filter-Kruskal Minimum Spanning Tree Algorithm. In: ALENEX, pp. 52–61. SIAM (2009)Google Scholar
  14. 14.
    Girvan, M., Newman, M.E.J.: Community structure in social and biological networks. Proc. Natl. Acad. Sci. U S A 99(12), 7821–7826 (2002)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Birnbaum, Z.W.: On the importance of different components in a multicomponent system. In: Multivariate Analysis - II, pp. 581–592 (1969)Google Scholar
  16. 16.
    Grötschel, M., Monma, C.L., Stoer, M.: Design of Survivable Networks. In: Handbooks in Operations Research and Management Science, vol. 7, pp. 617–672 (1995)Google Scholar
  17. 17.
    Faloutsos, C., McCurley, K.S., Tomkins, A.: Fast Discovery of Connection Subgraphs. In: KDD 2004: Proceedings of the Tenth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 118–127. ACM, New York (2004)CrossRefGoogle Scholar
  18. 18.
    Hintsanen, P., Toivonen, H.: Finding reliable subgraphs from large probabilistic graphs. Data Min. Knowl. Discov. 17, 3–23 (2008)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Toivonen, H., Zhou, F., Hartikainen, A., Hinkka, A.: Compression of Weighted Graphs. In: The 17th ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD), San Diego, CA, USA (2011)Google Scholar

Copyright information

© The Author(s) 2012 2012

Authors and Affiliations

  • Fang Zhou
    • 1
  • Sébastien Mahler
    • 1
  • Hannu Toivonen
    • 1
  1. 1.Department of Computer Science and HIITUniversity of HelsinkiFinland

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