This paper presents a Variable Neighborhood Search (VNS) based heuristic for hierarchical divisive edge-ratio network clustering. The edge-ratio criterion is used to identify communities in networks by maximizing the minimum ratio of inner edges to cut edges for both classes of a bipartition. The VNS heuristic is applied to perform community splitting in a hierarchical divisive algorithm. A k-neighborhood is defined as the movement of k entities, i.e., k entities change their membership from one to another cluster. A local search is based on 1-changes and k-changes are used for shaking the incumbent solution. Computational results on datasets from the literature validate the proposed approach. The VNS algorithm is efficient and provides good quality results with significantly reduced computational time compared to exact methods. The algorithm is tested on 11 datasets from the literature, including Zachary's karate club dataset, Lusseau's dolphins dataset, Hugo's Les Misérables dataset, Krebs' political books dataset, a dataset representing the schedule of football games between American college teams, a network dealing with connections between US airports, a dataset on a coauthorship network of scientists working on network theory and experiment, a network describing electronic circuits, a network representing e-mail interchanges between members of a university, a network giving the topology of the Western States Power Grid of the United States, and a network of authors collaborations. The results show that the VNS approach is effective in identifying communities in networks and provides results that are comparable to those obtained using exact methods. The algorithm is efficient and can be used to solve larger problems with respect to problems that can be solved using exact methods. The VNS approach is also compared with a locally optimal hierarchical divisive algorithm, and it is shown that the VNS approach provides results that are comparable to those obtained using exact methods. The algorithm is based on the edge-ratio criterion, which is an alternative approach to the modularity criterion. The VNS algorithm is efficient and provides good quality results with significantly reduced computational time compared to exact methods. The algorithm is tested on 11 datasets from the literature, and the results show that the VNS approach is effective in identifying communities in networks and provides results that are comparable to those obtained using exact methods.This paper presents a Variable Neighborhood Search (VNS) based heuristic for hierarchical divisive edge-ratio network clustering. The edge-ratio criterion is used to identify communities in networks by maximizing the minimum ratio of inner edges to cut edges for both classes of a bipartition. The VNS heuristic is applied to perform community splitting in a hierarchical divisive algorithm. A k-neighborhood is defined as the movement of k entities, i.e., k entities change their membership from one to another cluster. A local search is based on 1-changes and k-changes are used for shaking the incumbent solution. Computational results on datasets from the literature validate the proposed approach. The VNS algorithm is efficient and provides good quality results with significantly reduced computational time compared to exact methods. The algorithm is tested on 11 datasets from the literature, including Zachary's karate club dataset, Lusseau's dolphins dataset, Hugo's Les Misérables dataset, Krebs' political books dataset, a dataset representing the schedule of football games between American college teams, a network dealing with connections between US airports, a dataset on a coauthorship network of scientists working on network theory and experiment, a network describing electronic circuits, a network representing e-mail interchanges between members of a university, a network giving the topology of the Western States Power Grid of the United States, and a network of authors collaborations. The results show that the VNS approach is effective in identifying communities in networks and provides results that are comparable to those obtained using exact methods. The algorithm is efficient and can be used to solve larger problems with respect to problems that can be solved using exact methods. The VNS approach is also compared with a locally optimal hierarchical divisive algorithm, and it is shown that the VNS approach provides results that are comparable to those obtained using exact methods. The algorithm is based on the edge-ratio criterion, which is an alternative approach to the modularity criterion. The VNS algorithm is efficient and provides good quality results with significantly reduced computational time compared to exact methods. The algorithm is tested on 11 datasets from the literature, and the results show that the VNS approach is effective in identifying communities in networks and provides results that are comparable to those obtained using exact methods.