Voter model dynamics on networks with social features

Abstract

The study of collective human behaviour in theoretical and real social systems is fundamental to understand the role of the social influence in human-to-human interaction. The voter model has been extensively studied in this context because of its straightforward approach and feasible theoretical treatment. In this regard, we aim to investigate the collective behaviour based on the influence of different factors associated with micro-level social processes. For example, in the voter model, the behaviour of the average time needed to a complete consensus depends on the network structure. Then, we investigated, numerically and analytically, how social network topology can affect the evolution of the voter model dynamics. We considered the social features fitness, homophily and Euclidean distance between nodes as preferential attachment rules in evolving networks. We show that the fact that these social attributes change the topological structure of the network generates impacts on the behaviour of the voter model dynamics running on top of these substrates. However, our simulations aim to interesting findings. Surprisingly, despite the social features and geographic properties present in the investigated networks, the standard heterogeneous mean-field theory can accurately describe the voter model in these investigated networks. Our results show, on the one hand, a strong correlation between the consensus time calculated on these network models and the consensus time obtained for real social networks. It is also verified, on the other hand, an absence of correlation when we compared the synthetic networks with non-social real networks. This finding suggests that the characteristics of network models, such as fitness, homophily and Euclidean distance between nodes, artificially imposed by the preferential attachment rules of the models, can indeed play the role of real social features.