A Two-stage Stochastic Optimization Approach for Detecting Structurally Stable Clusters in Randomly Changing Graphs

We introduce a stochastic extension for the problem of finding nonhereditary subgraphs of maximum size in randomly changing graphs. The proposed formulation utilizes a two-stage stochastic optimization framework for identifying subgraphs whose structural properties can be preserved and repaired whenever the underlying graph's topology changes randomly. Particular focus is placed on finding nonhereditary subgraphs that represent a diameter-based clique relaxation known as an $s$ -club. A combinatorial branch-and-bound algorithm is developed and demonstrated to be computationally effective on various configurations of random and real-life graphs.