Annals of Operations Research

, Volume 249, Issue 1–2, pp 55–73

Detecting large risk-averse 2-clubs in graphs with random edge failures

  • Foad Mahdavi Pajouh
  • Esmaeel Moradi
  • Balabhaskar Balasundaram


Detecting large 2-clubs in biological, social and financial networks can help reveal important information about the structure of the underlying systems. In large-scale networks that are error-prone, the uncertainty associated with the existence of an edge between two vertices can be modeled by assigning a failure probability to that edge. Here, we study the problem of detecting large “risk-averse” 2-clubs in graphs subject to probabilistic edge failures. To achieve risk aversion, we first model the loss in 2-club property due to probabilistic edge failures as a function of the decision (chosen 2-club cluster) and randomness (graph structure). Then, we utilize the conditional value-at-risk (CVaR) of the loss for a given decision as a quantitative measure of risk for that decision, which is bounded in the model. More precisely, the problem is modeled as a CVaR-constrained single-stage stochastic program. The main contribution of this article is a new Benders decomposition algorithm that outperforms an existing decomposition approach on a test-bed of randomly generated instances, and real-life biological and social networks.


2-club Graph-based data mining Conditional value-at-risk Benders decomposition 


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Management Science and Information Systems DepartmentUniversity of Massachusetts BostonBostonUSA
  2. 2.School of Industrial Engineering and ManagementOklahoma State UniversityStillwaterUSA
  3. 3.Lee Scott Logistics ComplexBentonvilleUSA

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