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Bisociative Knowledge Discovery pp 179–198Cite as

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Simplification of Networks by Edge Pruning

Simplification of Networks by Edge Pruning

  • Fang Zhou5,
  • Sébastien Mahler5 &
  • Hannu Toivonen5 
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  • Open Access
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  • 20 Citations

  • 9 Altmetric

Part of the Lecture Notes in Computer Science book series (LNAI,volume 7250)

Abstract

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.

This chapter is a modified version of article “Network Simplification with Minimal Loss of Connectivity” in the 10th IEEE International Conference on Data Mining (ICDM), 2010 [1].

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References

  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. 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)

    CrossRef  Google Scholar 

  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)

    CrossRef  Google Scholar 

  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)

    CrossRef  Google Scholar 

  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)

    CrossRef  Google Scholar 

  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)

    CrossRef  MathSciNet  Google Scholar 

  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)

    CrossRef  Google Scholar 

  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)

    CrossRef  Google Scholar 

  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. 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)

    CrossRef  Google Scholar 

  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)

    CrossRef  Google Scholar 

  12. Toussaint, G.T.: The Relative Neighbourhood Graph of a Finite Planar Set. Pattern Recognition 12(4), 261–268 (1980)

    CrossRef  MathSciNet  Google Scholar 

  13. Osipov, V., Sanders, P., Singler, J.: The Filter-Kruskal Minimum Spanning Tree Algorithm. In: ALENEX, pp. 52–61. SIAM (2009)

    CrossRef  Google Scholar 

  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)

    CrossRef  MathSciNet  Google Scholar 

  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. 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. 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)

    CrossRef  Google Scholar 

  18. Hintsanen, P., Toivonen, H.: Finding reliable subgraphs from large probabilistic graphs. Data Min. Knowl. Discov. 17, 3–23 (2008)

    CrossRef  MathSciNet  Google Scholar 

  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 

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Authors and Affiliations

  1. Department of Computer Science and HIIT, University of Helsinki, Finland

    Fang Zhou, Sébastien Mahler & Hannu Toivonen

Authors
  1. Fang Zhou
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  2. Sébastien Mahler
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  3. Hannu Toivonen
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Editor information

Editors and Affiliations

  1. Department of Computer and Information Science, University of Konstanz, Konstanz, Germany

    Michael R. Berthold

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Zhou, F., Mahler, S., Toivonen, H. (2012). Simplification of Networks by Edge Pruning. In: Berthold, M.R. (eds) Bisociative Knowledge Discovery. Lecture Notes in Computer Science(), vol 7250. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31830-6_13

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