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On clique relaxation models in network analysis

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  • Pattillo, Jeffrey
  • Youssef, Nataly
  • Butenko, Sergiy
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    Abstract

    Increasing interest in studying community structures, or clusters in complex networks arising in various applications has led to a large and diverse body of literature introducing numerous graph-theoretic models relaxing certain characteristics of the classical clique concept. This paper analyzes the elementary clique-defining properties implicitly exploited in the available clique relaxation models and proposes a taxonomic framework that not only allows to classify the existing models in a systematic fashion, but also yields new clique relaxations of potential practical interest. Some basic structural properties of several of the considered models are identified that may facilitate the choice of methods for solving the corresponding optimization problems. In addition, bounds describing the cohesiveness properties of different clique relaxation structures are established, and practical implications of choosing one model over another are discussed.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0377221712007679
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    Bibliographic Info

    Article provided by Elsevier in its journal European Journal of Operational Research.

    Volume (Year): 226 (2013)
    Issue (Month): 1 ()
    Pages: 9-18

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    Handle: RePEc:eee:ejores:v:226:y:2013:i:1:p:9-18

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    Web page: http://www.elsevier.com/locate/eor

    Related research

    Keywords: Clique relaxations; Maximum clique problem; Social network analysis; Cohesive subgroups; Biological networks;

    References

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    1. R. Luce, 1950. "Connectivity and generalized cliques in sociometric group structure," Psychometrika, Springer, vol. 15(2), pages 169-190, June.
    2. Veremyev, Alexander & Boginski, Vladimir, 2012. "Identifying large robust network clusters via new compact formulations of maximum k-club problems," European Journal of Operational Research, Elsevier, vol. 218(2), pages 316-326.
    3. Boginski, Vladimir & Butenko, Sergiy & Pardalos, Panos M., 2005. "Statistical analysis of financial networks," Computational Statistics & Data Analysis, Elsevier, vol. 48(2), pages 431-443, February.
    4. Butenko, S. & Wilhelm, W.E., 2006. "Clique-detection models in computational biochemistry and genomics," European Journal of Operational Research, Elsevier, vol. 173(1), pages 1-17, August.
    5. Robert Mokken, 1979. "Cliques, clubs and clans," Quality & Quantity: International Journal of Methodology, Springer, vol. 13(2), pages 161-173, April.
    6. R. Luce & Albert Perry, 1949. "A method of matrix analysis of group structure," Psychometrika, Springer, vol. 14(2), pages 95-116, June.
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    Cited by:
    1. Svyatoslav Trukhanov & Chitra Balasubramaniam & Balabhaskar Balasundaram & Sergiy Butenko, 2013. "Algorithms for detecting optimal hereditary structures in graphs, with application to clique relaxations," Computational Optimization and Applications, Springer, vol. 56(1), pages 113-130, September.

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