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On clique relaxation models in network analysis

  • Pattillo, Jeffrey
  • Youssef, Nataly
  • Butenko, Sergiy
Registered author(s):

    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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    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
    Contact details of provider: Web page: http://www.elsevier.com/locate/eor

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    1. 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.
    2. James Moody & Douglas R. White, 2000. "Structural Cohesion and Embeddedness: A Hierarchical Conception of Social Groups," Working Papers 00-08-049, Santa Fe Institute.
    3. R. Luce & Albert Perry, 1949. "A method of matrix analysis of group structure," Psychometrika, Springer, vol. 14(2), pages 95-116, June.
    4. 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.
    5. R. Luce, 1950. "Connectivity and generalized cliques in sociometric group structure," Psychometrika, Springer, vol. 15(2), pages 169-190, June.
    6. Robert Mokken, 1979. "Cliques, clubs and clans," Quality & Quantity: International Journal of Methodology, Springer, vol. 13(2), pages 161-173, April.
    7. 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.
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