Identifying risk-averse low-diameter clusters in graphs with stochastic vertex weights

In this work, we study the problem of detecting risk-averse low-diameter clusters, modeled as k-clubs, in graphs. It is assumed that the uncertainty of the information associated with vertices is shown by stochastic weights, whose joint distribution is known. The goal is to find a k-club of minimum risk contained in the graph. A stochastic programming framework that is based on the formalism of coherent risk measures is used to find the corresponding cluster. The selected representation of risk of a cluster ensures that the optimal solutions are maximal k-clubs. A combinatorial branch-and-bound algorithm is proposed and solution performances are compared with an equivalent mathematical programming approach for instances with k D 2; 3; and 4.