Entangling mobility and interactions in social media

Przemyslaw A. Grabowicz1, José J. Ramasco1, Bruno Gonçalves2,3 and Victor M. Eguiluz1
1Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB), Palma de Mallorca, Spain.
2Aix-Marseille Université, CNRS, CPT, UMR 7332, 13288 Marseille, France.
3Université de Toulon, CNRS, CPT, UMR 7332, 83957 La Garde, France.

(July 2013)

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 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 the networks not captured by models uncoupling mobility and social interactions such as: i) the total 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 a simplified version of our 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.