A range of applications, from predicting the spread of human and electronic viruses to city planning and resource management in mobile communications, depend on our ability to foresee the whereabouts and mobility of individuals, raising a fundamental question: To what degree is human behavior predictable? Here we explore the limits of predictability in human dynamics by studying the mobility patterns of anonymized mobile phone users. By measuring the entropy of each individual's trajectory, we find a 93% potential predictability in user mobility across the whole user base. Despite the significant differences in the travel patterns, we find a remarkable lack of variability in predictability, which is largely independent of the distance users cover on a regular basis.

Complex networks have been studied extensively owing to their relevance to many real systems such as the world-wide web, the Internet, energy landscapes and biological and social networks. A large number of real networks are referred to as 'scale-free' because they show a power-law distribution of the number of links per node. However, it is widely believed that complex networks are not invariant or self-similar under a length-scale transformation. This conclusion originates from the 'small-world' property of these networks, which implies that the number of nodes increases exponentially with the 'diameter' of the network, rather than the power-law relation expected for a self-similar structure. Here we analyse a variety of real complex networks and find that, on the contrary, they consist of self-repeating patterns on all length scales. This result is achieved by the application of a renormalization procedure that coarse-grains the system into boxes containing nodes within a given 'size'. We identify a power-law relation between the number of boxes needed to cover the network and the size of the box, defining a finite self-similar exponent. These fundamental properties help to explain the scale-free nature of complex networks and suggest a common self-organization dynamics.

Uncovering the statistical patterns that characterize the trajectories humans follow during their daily activity is not only a major intellectual challenge, but also of importance for public health 1-5 , city planning 6-8 , traffic engineering 9, 10 and economic forecasting 11 . For example, quantifiable models of human mobility are indispensable for predicting the spread of biological pathogens 1-5 or mobile phone viruses 12 .In the past few years the availability of mobile phone records, GPS data, and other datasets capturing aspects of human mobility have given a new empirically driven momentum to the subject. While the available datasets significantly differ in their reach and resolution, the results appear to agree on a number of quantitative characteristics of human mobility. For example, both dollar bill tracking 13 and mobile phone data 14 indicate that the