A model of spatially constrained social network dynamics

Social networks characterise the set of relationships amongst a population of social agents. As such, their structure both constrains and is constrained by social processes such as partnership formation and the spread of information, opinions and behaviour. Models of these coevolutionary network dynamics exist, but they are generally limited to specific interaction types such as games on networks or opinion dynamics. Here we present a dynamic model of social network formation and maintenance that exhibits the characteristic features of real-world social networks such as community structure, high clustering, positive degree assortativity and short characteristic path length. While these macro-structural network properties are stable, the network micro-structure undergoes continuous change at the level of relationships between individuals. Notably, the edges are weighted, allowing for gradual change in relationship strength in contrast to more abrupt mechanisms, such as rewiring, used in other models. We show how the structural features that characterise social networks can arise as the result of constraints placed on the interactions between individuals. Here we explore the relationship between structural properties and four idealised constraints placed on social interactions: space, affinity, time, and history. We show that spatial embedding and the subsequent constraints on possible interactions are crucial in this model for the emergence of the structures characterising social networks.