- Anastasios Noulas ,
- Salvatore Scellato,
- Renaud Lambiotte,
- Massimiliano Pontil,
- Cecilia Mascolo
Since the seminal works of Ravenstein , the movement of people in space has been an active subject of research in the social and geographical sciences. It has been shown in almost every quantitative study and described in a broad range of models that a close relationship exists between mobility and distance. People do not move randomly in space, as we know from our daily lives. Human movements exhibit instead high levels of regularity and tend to be hindered by geographical distance. The origin of this dependence of mobility on distance, and the formulation of quantitative laws explaining human mobility remains, however, an open question, the answer of which would lead to many applications, e.g. improve engineered systems such as cloud computing and location-based recommendations –, enhance research in social networks – and yield insight into a variety of important societal issues, such as urban planning and epidemiology –.
In classical studies, two related but diverging viewpoints have emerged. The first camp argues that mobility is directly deterred by the costs (in time and energy) associated to physical distance. Inspired by Newton's law of gravity, the flow of individuals is predicted to decrease with the physical distance between two locations, typically as a power-law of distance –. Besides distance, more complex versions of gravity models may also consider a parameter that captures the “mass” of the starting point and the destination of a trip. In this case, usually the population of an area is used as a proxy to quantify it. These so-called “gravity-models” have a long tradition in quantitative geography and urban planning and have been used to model a wide variety of social systems, e.g. human migration , inter-city communication  and traffic flows . The second camp argues instead that there is no direct relation between mobility and distance, and that distance is a surrogate for the effect of intervening opportunities. The migration from origin to destination is assumed to depend on the number of opportunities closer than this destination. A person thus tends to search for destinations where to satisfy the needs giving rise to its journey, and the absolute value of their distance is irrelevant. Only their ranking matters. Displacements are thus driven by the spatial distribution of places of interest, and thus by the response to opportunities rather than by transport impedance as in gravity models. The first camp appears to have been favoured by practitioners on the grounds of computational ease , despite the fact that several statistical studies have shown that the concept of intervening opportunities is better at explaining a broad range of mobility data –.
This long-standing debate is of particular interest in view of the recent revival of empirical research on human mobility. Contrary to traditional works, where researchers have relied on surveys, small-scale observations or aggregate data, recent research has taken advantage of the advent of pervasive technologies in order to uncover trajectories of millions of individuals with unprecedented resolution and to search for universal mobility patterns, such to feed quantitative modelling. Interestingly, those works have all focused on the probabilistic nature of movements in terms of physical distance. As for gravity models, this viewpoint finds its roots in Physics, in the theory of anomalous diffusion. It tends to concentrate on the distributions of displacements as a function of geographic distance. Recent studies suggest the existence of a universal power-law distribution , observed for instance in cell tower data of humans carrying mobile phones  or in the movements of “Where is George” dollar bills . This universality is, however, in contradiction with observations that displacements strongly depend on where they take place. For instance, a study of hundreds of thousands of cell phones in Los Angeles and New York demonstrate different characteristic trip lengths in the two cities . This observation suggests either the absence of universal patterns in human mobility or the fact that physical distance is not a proper variable to express it.
In this work, we address this problem by focusing on human mobility patterns in a large number of cities across the world. More precisely, we aim at answering the following question: “Do people move in a substantially different way in different cities or, rather, do movements exhibit universal traits across disparate urban centers?”. To do so, we take advantage of the advent of mobile location-based social services accessed via GPS-enabled smartphones, for which fine granularity data about human movements is becoming available. Moreover, the worldwide adoption of these tools implies that the scale of the datasets is planetary. Exploiting data collected from public check-ins made by users of the most popular location-based social network, Foursquare , we study the movements of 925,030 users around the globe over a period of about six months, and study the movements across 5 million places in 34 metropolitan cities that span four continents and eleven countries.