Edge-ratio network clustering by Variable Neighborhood Search

The analysis of networks and in particular the identification of communities, or clusters, is a topic of active research with applications arising in many domains. Several models were proposed for this problem. In reference [S. Cafieri, P. Hansen, L. Liberti, Phys. Rev. E 81, 026105 (2010)], a criterion is proposed for a graph bipartition to be optimal: one seeks to maximize the minimum for both classes of the bipartition of the ratio of inner edges to cut edges (edge-ratio), and it is used in a hierarchical divisive algorithm for community identification in networks. In this paper, we develop a VNS-based heuristic for hierarchical divisive edge-ratio network clustering. A k-neighborhood is defined as move 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