Community detection, with lower time complexity, using coupled Kuramoto oscillators

Abstract

For about two decades, the research topic of Complex Networks has been presented ubiquitously. As a simple and effective framework to express agents and their relationships, several fields of study, from Physics to Sociology, have taken advantage of the powerful representation provided by complex networks. A particular feature inherited by almost any real world network is the presence of densely connected groups of vertices, named modules, clusters or communities. The majority of the proposed techniques does not take advantage of specific features commonly encountered on real networks, such as the power law distribution of vertices' degree (presence of hubs) and its dynamic nature, i.e. vertices, edges and communities normally does not persist invariant regarding to time. Aiming to take into account these two important features, an another ubiquitous phenomenon is applied on detecting communities: synchronization, expressed by coupled Kuramoto oscillators. Here, we extend the Kuramoto's model by introducing a negative coupling between hubs in the network. Moreover, two adjacency lists are used to represent, efficiently, the network structure. Tests have been performed in real network benchmarks, with consistent results achieved.