Coevolution in social networks

Abstract

Networks are thought to be essential in understanding the emergence and sustainability of collective behaviour in many complex systems often found in fields such as physics, sociology, biology, ecology and economy, to name just a few. The problem is that although they can be represented mathematically as a graph, the characterisation of nodes and links in it is usually quite arbitrary, and therefore basic quantities such as space dimension and metrics are not well defined, which leads to ambiguities in the establishment of dynamical equations to dictate the state of the system. In this paper we propose and review a general framework to study the dynamical evolution of networks based in the concept of coevolution, which implies a feedback between the state variables defined over the nodes and the structure of the network itself. The usefulness and generality of such a framework is shown by modelling an opinion formation process in human societies, in which the dynamical formation of community structures is predicted and characterised in terms of the parameters of the model.