The paper "Edge-Ratio Network Clustering by Variable Neighborhood Search" by Sonia Cafieri, Pierre Hansen, and Nenad Mladenovic introduces a heuristic method for hierarchical divisive edge-ratio network clustering. The authors propose a Variable Neighborhood Search (VNS) metaheuristic to solve the optimization problem of maximizing the edge ratio, which is defined as the ratio of inner edges to cut edges in a bipartition of a graph. The VNS algorithm iteratively explores neighborhoods of the current solution, performs local searches, and uses shaking procedures to perturb the incumbent solution. The effectiveness of the proposed method is validated through computational experiments on various datasets from the literature, demonstrating its ability to produce high-quality partitions while significantly reducing computational time compared to exact methods. The results are compared with those obtained using the modularity criterion and a locally optimal hierarchical divisive algorithm, showing that the VNS-based approach is both efficient and effective.The paper "Edge-Ratio Network Clustering by Variable Neighborhood Search" by Sonia Cafieri, Pierre Hansen, and Nenad Mladenovic introduces a heuristic method for hierarchical divisive edge-ratio network clustering. The authors propose a Variable Neighborhood Search (VNS) metaheuristic to solve the optimization problem of maximizing the edge ratio, which is defined as the ratio of inner edges to cut edges in a bipartition of a graph. The VNS algorithm iteratively explores neighborhoods of the current solution, performs local searches, and uses shaking procedures to perturb the incumbent solution. The effectiveness of the proposed method is validated through computational experiments on various datasets from the literature, demonstrating its ability to produce high-quality partitions while significantly reducing computational time compared to exact methods. The results are compared with those obtained using the modularity criterion and a locally optimal hierarchical divisive algorithm, showing that the VNS-based approach is both efficient and effective.