Zipf's law for all the natural cities in the United States: a geospatial perspective

This article provides a new geospatial perspective on whether or not Zipf's law holds for all cities or for the largest cities in the United States using a massive dataset and its computing. A major problem around this issue is how to define cities or city boundaries. Most of the investigations of Zipf's law rely on the demarcations of cities imposed by census data, for example, metropolitan areas and census-designated places. These demarcations or definitions (of cities) are criticized for being subjective or even arbitrary. Alternative solutions to defining cities are suggested, but they still rely on census data for their definitions. In this article we demarcate urban agglomerations by clustering street nodes (including intersections and ends), forming what we call natural cities. Based on the demarcation, we found that Zipf's law holds remarkably well for all the natural cities (over 2-4 million in total) across the United States. There is little sensitivity for the holding with respect to the clustering resolution used for demarcating the natural cities. This is a big contrast to urban areas, as defined in the census data, which do not hold stable for Zipf's law.