Identification of Chordless Cycles in Ecological Networks

  • Nayla Sokhn
  • Richard Baltensperger
  • Louis-Félix Bersier
  • Jean Hennebert
  • Ulrich Ultes-Nitsche
Part of the Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering book series (LNICST, volume 126)


In the last few years the studies on complex networks have gained extensive research interests. Significant impacts are made by these studies on a wide range of different areas including social networks, technology networks, biological networks and others. Motivated by understanding the structure of ecological networks we introduce in this paper a new algorithm for enumerating all chordless cycles. The proposed algorithm is a recursive one based on the depth-first search.


ecological networks community structure food webs niche-overlap graphs chordless cycles 


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  1. 1.
    Cohen, J.: Food Webs and Niche Space. Princeton University Press, Princeton (1978)Google Scholar
  2. 2.
    Sugihara, G.: Niche Hierarchy: Structure Assembly and Organization in Natural Communities. PhD thesis, Princeton University, Princeton (1982)Google Scholar
  3. 3.
    Cohen, J., Briand, F., Newman, C.: Community Food Webs, Data and Theory. Springer (1990)Google Scholar
  4. 4.
    Bersier, L.F., Baltensperger, R., Gabriel, J.P.: Why are cordless cycles so common in niche overlap graphs? In: Ecological Society of America, Annual Meeting, p. 76 (2002)Google Scholar
  5. 5.
    Huxham, M., Beaney, S., Raffaelli, D.: Do parasites reduce the changes of triangulation in a real food web? Oikos 76, 284–300 (1996)CrossRefGoogle Scholar
  6. 6.
    Golumbic, M.: Algorithmic graph theory and perfect graphs, 2nd edn. Elsevier (2004)Google Scholar
  7. 7.
    Mateti, P., Deo, N.: On algorithms for enumerating all circuits of a graph. SIAM J. Comput. 5, 90–99 (1976)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Tiernan, J.: An efficient search algorithm to find the elementary circuits of a graph. Communications of the ACM 13, 722–726 (1970)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Tarjan, R.: Enumeration of the elementary circuits of a directed graph. SIAM J. Comput. 2, 211–216 (1973)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Liu, H., Wang, J.: A new way to enumerate cycles in graph. In: AICT/ICIW, pp. 57–59 (2006)Google Scholar
  11. 11.
    Sankar, K., Sarad, A.: A time and memory efficient way to enumerate cycles in a graph. In: ICIAS, pp. 498–500 (2007)Google Scholar
  12. 12.
    Johnson, D.: Find all the elementary circuits of a directed graph. SIAM J. Comput. 4, 77–84 (1977)CrossRefGoogle Scholar
  13. 13.
    Spinrad, J.: Finding large holes. Inform. Process. Lett. 39, 227–229 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Nikolopoulos, S., Palios, L.: Hole and antihole detection in graphs. In: Proc. 15th ACM-SIAM Sympos. Discrete Algorithms, pp. 843–852 (2004)Google Scholar
  15. 15.
    Hayward, R.: Weakly triangulated graphs. J. Combinatorial Theory Series B 39, 200–208 (1985)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Bisdorff, R.: On enumerating chordless circuits in directed graphs,
  17. 17.
    Epp, S.: Discrete mathematics with applications, 2nd edn. Brooks/Cole Publishing Company (1995)Google Scholar

Copyright information

© ICST Institute for Computer Science, Social Informatics and Telecommunications Engineering 2013

Authors and Affiliations

  • Nayla Sokhn
    • 1
    • 2
  • Richard Baltensperger
    • 2
  • Louis-Félix Bersier
    • 1
  • Jean Hennebert
    • 1
    • 2
  • Ulrich Ultes-Nitsche
    • 1
  1. 1.University of FribourgFribourgSwitzerland
  2. 2.University of Applied Sciences of Western SwitzerlandFribourgSwitzerland

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