https://enac.hal.science/hal-00979295Cafieri, SoniaSoniaCafieriMAIAA - ENAC - Laboratoire de Mathématiques Appliquées, Informatique et Automatique pour l'Aérien - ENAC - Ecole Nationale de l'Aviation CivileHansen, PierrePierreHansenHEC Montréal - HEC MontréalMladenovic, NenadNenadMladenovicDepartment of Mathematical Sciences [Brunel] - Brunel University London [Uxbridge]Edge-Ratio Network Clustering by Variable Neighborhood SearchHAL CCSD2014statistical and nonlinear physics[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]Smith, Céline2014-04-15 16:21:022021-12-13 11:34:062014-04-15 16:29:12enJournal articleshttps://enac.hal.science/hal-00979295/document10.1140/epjb/e2014-50026-4application/pdf1The analysis of networks and in particular the identification of communities, or clusters, is a topic of active research with application arising in many domains. Several models were proposed for its solution. In [Cafieri et al., Phys. Rev. E 81(2):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.