  Daily interactions naturally define social circles. Individuals tend to be
friends with the people they spend time with and they choose to spend time with
their friends, inextricably entangling physical location and social
relationships. As a result, it is possible to predict not only someone's
location from their friends' locations but also friendship from spatial and
temporal co-occurrence. While several models have been developed to separately
describe mobility and the evolution of social networks, there is a lack of
studies coupling social interactions and mobility. In this work, we introduce a
new model that bridges this gap by explicitly considering the feedback of
mobility on the formation of social ties. Data coming from three online social
networks (Twitter, Gowalla and Brightkite) is used for validation. Our model
reproduces various topological and physical properties of these networks such
as: i) the size of the connected components, ii) the distance distribution
between connected users, iii) the dependence of the reciprocity on the
distance, iv) the variation of the social overlap and the clustering with the
distance. Besides numerical simulations, a mean-field approach is also used to
study analytically the main statistical features of the networks generated by
the model. The robustness of the results to changes in the model parameters is
explored, finding that a balance between friend visits and long-range random
connections is essential to reproduce the geographical features of the
empirical networks.
