Previous studies demonstrated empirically that human mobility exhibits Lévy flight behavior. However, our knowledge of the mechanisms governing this Lévy flight behavior remains limited. Here we analyze over $72000$ people’s moving trajectories, obtained from 50 taxicabs during a six-month period in a large street network, and illustrate that the human mobility pattern, or the Lévy flight behavior, is mainly attributed to the underlying street network. In other words, the goal-directed nature of human movement has little effect on the overall traffic distribution. We further simulate the mobility of a large number of random walkers and find that (1) the simulated random walkers can reproduce the same human mobility pattern, and (2) the simulated mobility rate of the random walkers correlates pretty well (an $R$ square up to 0.87) with the observed human mobility rate.

Although geographic features, such as mountains and coastlines, are fractal, some studies have claimed that the fractal property is not universal. This claim, which is false, is mainly attributed to the strict definition of fractal dimension as a measure or index for characterizing the complexity of fractals. In this paper, we propose an alternative, the ht-index, to quantify the fractal or scaling structure of geographic features. A geographic feature has ht-index h if the pattern of far more small things than large ones recurs (h-1) times at different scales. The higher the ht-index, the more complex the geographic feature. We conduct three case studies to illustrate how the computed ht-indices capture the complexity of different geographic features. We further discuss how the ht-index is complementary to fractal dimension, and elaborate on a dynamic view behind the ht-index that enables better understanding of geographic forms and processes. Keywords: Scaling of geographic space, fractal dimension, Richardson plot, nested rank-size plots, and head/tail breaksComment: 13 pages, 8 figures, 3 tables, minor revision on figure 1, new color ramp for figure

Two fundamental issues surrounding research on Zipf’s law regarding city sizes are whether and why this law holds. This paper does not deal with the latter issue with respect to why, and instead investigates whether Zipf’s law holds in a global setting, thus involving all cities around the world. Unlike previous studies, which have mainly relied on conventional census data such as populations and census-bureau-imposed definitions of cities, we adopt naturally (in terms of data speak for itself) delineated cities, or natural cities, to be more precise, in order to examine Zipf’s law. We find that Zipf’s law holds remarkably well for all natural cities at the global level, and it remains almost valid at the continental level except for Africa at certain time instants. We further examine the law at the country level, and note that Zipf’s law is violated from country to country or from time to time. This violation is mainly due to our limitations; we are limited to individual countries, or to a static view on city-size distributions. The central argument of this paper is that Zipf’s law is universal, and we therefore must use the correct scope in order to observe it. We further find Zipf’s law applied to city numbers; the number of cities in the largest country is twice as many as that in the second largest country, three times as many as that in the third largest country, and so on. These findings have profound implications for big data and the science of cities.

Existing urban boundaries are usually defined by government agencies for administrative, economic, and political purposes. However, it is not clear whether the boundaries truly reflect human interactions with urban space in intra- and interregional activities. Defining urban boundaries that consider socioeconomic relationships and citizen commute patterns is important for many aspects of urban and regional planning. In this paper, we describe a method to delineate urban boundaries based upon human interactions with physical space inferred from social media. Specifically, we depicted the urban boundaries of Great Britain using a mobility network of Twitter user spatial interactions, which was inferred from over 69 million geo-located tweets. We define the non-administrative anthropographic boundaries in a hierarchical fashion based on different physical movement ranges of users derived from the collective mobility patterns of Twitter users in Great Britain. The results of strongly connected urban regions in the form of communities in the network space yield geographically cohesive, nonoverlapping urban areas, which provide a clear delineation of the non-administrative anthropographic urban boundaries of Great Britain. The method was applied to both national (Great Britain) and municipal scales (the London metropolis). While our results corresponded well with the administrative boundaries, many unexpected and interesting boundaries were identified. Importantly, as the depicted urban boundaries exhibited a strong instance of spatial proximity, we employed a gravity model to understand the distance decay effects in shaping the delineated urban boundaries. The model explains how geographical distances found in the mobility patterns affect the interaction intensity among different non-administrative anthropographic urban areas, which provides new insights into human spatial interactions with urban space.

A number of recent studies showed that digital footprints around built environments, such as geo-located tweets, are promising data sources for characterizing urban land use. However, challenges for achieving this purpose exist due to the volume and unstructured nature of geo-located social media. Previous studies focused on analyzing Twitter data collectively resulting in coarse resolution maps of urban land use. We argue that the complex spatial structure of a large collection of tweets, when viewed through the lens of individual-level human mobility patterns, can be simplified to a series of key locations for each user, which could be used to characterize urban land use at a higher spatial resolution. Contingent issues that could affect our approach, such as Twitter users’ biases and tendencies at locations where they tweet the most, were systematically investigated using 39 million geo-located Tweets and two independent datasets of the City of Chicago: 1) travel survey and 2) parcel-level land use map. Our results support that the majority of Twitter users show a preferential return, where their digital traces are clustered around a few key locations. However, we did not find a general relation among users between the ranks of locations for an individual—based on the density of tweets—and their land use types. On the contrary, temporal patterns of tweeting at key locations were found to be coherent among the majority of users and significantly associated with land use types of these locations. Furthermore, we used these temporal patterns to classify key locations into generic land use types with an overall classification accuracy of 0.78. The contribution of our research is twofold: a novel approach to resolving land use types at a higher resolution, and in-depth understanding of Twitter users’ location-related and temporal biases, promising to benefit human mobility and urban studies in general.