Effects of homophily and heterophily on preferred-degree networks: mean-field analysis and overwhelming transition ; Journal of Statistical Mechanics-Theory and Experiment

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, 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 investigate how the sizes of the communities and the degree of homophily/heterophily affect 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 the larger group, and their mean degree greatly exceeds the preferred degree. This and related phenomena are characterized by the network's total and joint degree distributions, as well as the fraction of links across both communities and that of agents having fewer edges than the preferred degree. We use our mean-field theory to discuss the network's polarization when the group sizes and level of homophily vary. ; Chinese Scholarship Council [201803170212]; University of Leeds [201803170212]; London Mathematical Society [41712]; Leeds School of Mathematics ; Published version ; We are indebted and grateful to Andrew Mellor for substantial input and helpful discussions. The support of a joint PhD studentship of the Chinese Scholarship Council and University of Leeds to X L is gratefully acknowledged (Grant No. 201803170212). We are also grateful to the London Mathematical Society (Grant No. 41712) and Leeds School of Mathematics for their financial support, and R K P Z is thankful to the Leeds School of Mathematics for their hospitality at an early stage of this collaboration. This work was undertaken on ARC4, part of the High Performance Computing facilities at ...