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 decomposition algorithm based on a Benders decomposition scheme, which outperforms an algorithm based on an existing decomposition idea, on a test-bed of randomly generated instances, and real-life biological and social networks.