The advent of geographic online social networks such as Foursquare, where users voluntarily signal their current location, opens the door to powerful studies on human movement. In particular the fine granularity of the location data, with GPS accuracy down to 10 meters, and the worldwide scale of Foursquare adoption are unprecedented. In this paper we study urban mobility patterns of people in several metropolitan cities around the globe by analyzing a large set of Foursquare users. Surprisingly, while there are variations in human movement in different cities, our analysis shows that those are predominantly due to heterogeneous distribution of places across different urban environments. Moreover, a universal law for human mobility is identified, which isolates the rank distance as a key component, factoring in the number of places between origin and destination, rather than pure physical distance, as considered in previous works. Building on our findings, we also show that a rank-based movement accurately captures real human movements in different cities. Our results shed new light on the driving factors of urban human mobility, with potential applications to urban planning, location-based advertisement and even social studies. Since the seminal works of Ravenstein [1], 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 [2-5], enhance research in social networks [6] [7] [8] [9] and yield insight into a variety of important societal issues, such as urban planning and epidemiology [10] [11] [12] . 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 [13] [14] [15] . 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 [16] , inter-city communication [17] and traffic flows [18] . 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 [19] . 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 [20] , 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 [21] [22] [23] [24] [25] . 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 P (∆r) ∼ ∆r −β , observed for instance in cell tower data of humans carrying mobile phones β = 1.75 [26] or in the movements of "Where is George" dollar bills β = 1.59 [27] . 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 [28] . 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 arXiv:1108.5355v4 [physics.soc-ph]
They further identify universal features for human urban mobility REF .
A tale of many cities: universal patterns in human urban mobility
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