Applications of Hypergraph Theory: A Brief Overview

  • Alain Bretto
Part of the Mathematical Engineering book series (MATHENGIN)


Like in most fruitful mathematical theories, the theory of hypergraphs has many applications. Hypergraphs model many practical problems in many different sciences. it makes very little time (20 years) that the theory of hypergraphs is used to model situations in the applied sciences. We find this theory in psychology, genetics, \(\ldots \) but also in various human activities. Hypergraphs have shown their power as a tool to understand problems in a wide variety of scientific field. Moreover it well known now that hypergraph theory is a very useful tool to resolve optimization problems such as scheduling problems, location problems and so on. This chapter shows some possible uses of hypergraphs in Applied Sciences.


  1. [KS01]
    E.V. Konstantinova, V.A. Skorobogatov, Application of hypergraph theory in chemistry. Discret. Math. 235(1–3), 365–383 (2001)Google Scholar
  2. [KHT09]
    S. Klamt, U.U. Haus, F.J. Theis, Hypergraphs and cellular networks. PLoS Comput. Biol. 5(5), e1000385 (2009)Google Scholar
  3. [HK00]
    B. Hendrickson, T.G. Kolda, Graph partitioning models for parallel computing. Parallel Comput. 26, 1519–1545 (2000)MathSciNetMATHCrossRefGoogle Scholar
  4. [Fag83]
    R. Fagin, Degrees of acyclicity for hypergraphs and relational database systems. J. Assoc. Comput. Mach. 30, 514–550 (1983)MathSciNetMATHCrossRefGoogle Scholar
  5. [HBC07]
    C. Hébert, A. Bretto, B. Crémilleux, A data mining formalization to improve hypergraph minimal transversal computation. Fundamenta Informaticae 80(4), 415–433 (2007)MathSciNetMATHGoogle Scholar
  6. [BG05]
    A. Bretto and L. Gillibert. Hypergraph-based Image Representation, in GbRPR of Lecture Notes in Computer Science, vol. 3434 (Springer, 2005), pp. 1–11Google Scholar
  7. [DBRL12]
    A. Ducournau, A. Bretto, S. Rital, B. Laget, A reductive approach to hypergraph clustering: An application to image segmentation. Pattern Recogn. 45(7), 2788–2803 (2012)MATHCrossRefGoogle Scholar
  8. [HOS12]
    Marc Hellmuth, Lydia Ostermeier, Peter F. Stadler, A survey on hypergraph products. Math. Comput. Sci. 6(1), 1–32 (2012)MathSciNetCrossRefGoogle Scholar
  9. [Rob39]
    H.E. Robbins, A theorem on graphs with an application to a problem of traffic control. Am. Math. Mon. 46, 281–283 (1939)MathSciNetCrossRefGoogle Scholar
  10. [STV04]
    B. SchÃülkopf, K. Tsuda, J.P. Vert, Kernel Methods in Computational Biology. (MIT Press, 2004)Google Scholar
  11. [Smo07]
    S. Smorodinsky, On the chromatic number of geometric hypergraphs. SIAM J. Discret. Math. 21(3), 676–687 (2007)MathSciNetMATHCrossRefGoogle Scholar
  12. [Zyk74]
    A.A. Zykov, Hypergraphs. Uspekhi Mat. Nauk. 29, 89–154 (1974)MathSciNetGoogle Scholar
  13. [BP09]
    S.R. Bulò, M. Pelillo, A Game-Theoretic Approach to Hypergraph Clustering, in proceedings of the NIPS, pp. 1571–1579 (2009)Google Scholar
  14. [Sla78]
    P.J. Slater, A characterization of soft hypergraphs. Can. Math. Bull. 21, 335–337 (1978)MathSciNetMATHCrossRefGoogle Scholar
  15. [Gol11]
    O. Goldreich. Using the Fglss-Reduction to Prove Inapproximability Results for Minimum Vertex Cover in Hypergraphs, in Studies in Complexity and Cryptography, pp. 88–97 (2011)Google Scholar
  16. [Bre04]
    A. Bretto, Introduction to Hypergraph Theory and their Use in Engeneering and Image Processing. Advances in Imaging and Electron Physics (Monographic Series) (Elsevier Academic Press, 2004)Google Scholar
  17. [Hua08]
    L. Huang, Advanced dynamic programming in semiring and hypergraph frameworks (2008)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  1. 1.Computer Science DepartmentUniversite de CaenCaenFrance

Personalised recommendations