Scaling Behaviors in the Communication Network between Cities

Abstract

Researchers have been unable to predict the large-scale features of aggregate social networks. We analyze the anonymous communications patterns of 2.5 million customers of a Belgian mobile phone operator. With these communications, we construct the social network of the customers, that we call microscopic network. Grouping customers together by billing address city, we obtain a social network of cities, which we call the macroscopic network, is built from 571 towns and cities in Belgium. Using the mobile phone network, we are able to show that the macroscopic network has both a degree distribution and edge weight distribution with lognormal characteristics. We find that inter-city communications can be characterized by a gravity model: the intensity of communication between two cities is proportional to the product of the two populations divided by the square of the distance between them. Furthermore, we observe that intra-urban communications scale superlinearly with city population.