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We investigate the long-time properties of a dynamic, out-of-equilibrium, network of individuals holding one of two opinions in a population consisting of two communities of different sizes. Here, while the agents opinions are fixed, they have a preferred degree which leads them to endlessly create and delete links. Our evolving network is shaped by homophily/heterophily, which is a form of social interaction by which individuals tend to establish links with others having similar/dissimilar opinions. Using Monte Carlo simulations and a detailed mean-field analysis, we study in detail how the sizes of the communities and the degree of homophily/heterophily affects the network structure. In particular, we show that when the network is subject to enough heterophily, an overwhelming transition occurs: individuals of the smaller community are overwhelmed by links from agents of the larger group, and their mean degree greatly exceeds the preferred degree. This and related phenomena are characterized by obtaining the networks total and joint degree distributions, as well as the fraction of links across both communities and that of agents having less edges than the preferred degree. We use our mean-field theory to discuss the networks polarization when the group sizes and level of homophily vary.
We propose a generalized framework for the study of voter models in complex networks at the the heterogeneous mean-field (HMF) level that (i) yields a unified picture for existing copy/invasion processes and (ii) allows for the introduction of furthe
We study a simple model of dynamic networks, characterized by a set preferred degree, $kappa$. Each node with degree $k$ attempts to maintain its $kappa$ and will add (cut) a link with probability $w(k;kappa)$ ($1-w(k;kappa)$). As a starting point, w
Mean-field analysis is an important tool for understanding dynamics on complex networks. However, surprisingly little attention has been paid to the question of whether mean-field predictions are accurate, and this is particularly true for real-world
We present a detailed investigation of the behavior of the nonlinear q-voter model for opinion dynamics. At the mean-field level we derive analytically, for any value of the number q of agents involved in the elementary update, the phase diagram, the
We study the robustness properties of multiplex networks consisting of multiple layers of distinct types of links, focusing on the role of correlations between degrees of a node in different layers. We use generating function formalism to address var