Modelling behaviour in author networks with graphon mean field games

Abstract Whenever many people interact, as on social media, their behaviour can be described as a network. Existing research mainly focuses on the characteristics of different networks or the importance of connections. For example, previous research has established that people strive for as many connections to others as possible, as this provides access to more resources and information. However, the relationship between the pursuit of connections in a network and an individual’s behaviour remains largely unknown. Here we show that people’s behaviour correlates with the number of their connections. We analysed an author network’s user behaviour, measured by the explicitness of their works, with respect to their connectedness and reconstructed their behaviour using a graphon mean field game. The data show that the explicitness of an author’s published texts correlates with the number of connections to other participants in the network. Our model shows that this correlation cannot be explained by the greater popularity of explicit content alone, but also requires consideration of the influence of an author’s neighbourhood. Our results demonstrate that individuals not only strive for connections in networks, but their behaviour is linked to their interaction with the crowd. Hence, to describe the behaviour of individuals in a crowd, their connectedness should be considered. We hope this work opens up a new direction in analysing social networks. For one, our results show that people’s behaviour is linked to their neighbourhood in a network. Moreover, the graphon mean field game we employ provides a mathematical description of human behaviour in crowds, which can be used to investigate and model various influences on behaviour quantitatively.