A universal law in human mobility

The intrinsic factor that drives the human movement remains unclear for decades. While our observations from intra-urban and inter-urban trips both demonstrate a universal law in human mobility. Be specific, the probability from one location to another is inversely proportional to the number of population living in locations which are closer than the destination. A simple rank-based model is then presented, which is parameterless but predicts human flows with a convincing fidelity. Besides, comparison with other models shows that our model is more stable and fundamental at different spatial scales by implying the strong correlation between human mobility and social relationship. Introduction In recent years, there are increasing available human trajectories collected by diverse “sensors”, which provide us opportunities to gain deeper insight into human mobility patterns. Specifically, there are some empirical studies on human mobility with the help of distinct “sensors” for track data acquisition such as banknotes [1], cellular towers [2–5], GPS [6–8] and online location-based social services [1,2,10]. Though these studies have greatly improved our understanding of human mobility patterns, there is still lack of a unified framework to explain and model human mobility. First, studied mobility datasets collected by different acquisition techniques often capture different population groups’ movements at different spatial scales or resolutions in different geographical environments. Therefore, some inconsistent results are observed. For example, heavy-tailed [1, 2] and exponential [4, 7, 8, 12–14] distributions of human trip lengths are observed at the intra-urban and inter-urban levels respectively. Some research thinks the exponential law is emerged in trips captured by a single means of transportation while the scaling law in movements by various kinds of transportation modes [15, 16]. However, another study attributes the different laws to different geographical population distributions at different spatial scales [17]. Second, many agent-based mobility models [1, 3, 18–20] are proposed to model individual movements, which try to reproduce some features observed at the aggregated level. But the diversity of individual mobility patterns is discovered recently [16] and a general understanding of human movements is still missed. Third, for collective movements, the gravity model [21] is widely used to predict human flows [22–24]. But the parameters in the model must be fitted from actual flux in advance. In addition, the model cannot explain the asymmetry of traffic flows between any two locations. Then the radiation model [25] is proposed to deepen our understanding of human mobility, which is nonparametric and suitable for predicting commuting and migration flows. However, it is restricted by movements datasets [26] and is incompetent to characterize human daily movements at the intra-urban level [17, 27]. Because of this, there are new studies aiming to model human flows in cities [17, 27]. To be brief, all the above reasons make putting forward a general model for both intra-urban and inter-urban mobility necessary, which is exactly the aim of the present work. In this paper, we explore human travels at different spatial scales and try to unify the understanding of general human mobility patterns. First of all, a universal law for human mobility is demonstrated at intraurban and inter-urban levels. Then based on the universal law we propose a rank-based mobility model that is parameter-free, enabling us to predict human flows only depending on geographical population distribution. Finally, we compare some recent mobility models and suggest that the rank-based model is more simple, stable and fundamental. Most of important, it could bridge human mobility and social