Zipfs Law for All the Natural Cities in the United States: A Geospatial Perspective

This paper 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, e.g., 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 paper 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. Keywords: Natural cities, power law, data-intensive geospatial computing, scaling of geographic space

💡 Research Summary

This paper examines whether Zipf’s law holds for all cities or the largest cities in the United States from a new geospatial perspective. Traditionally, studies on Zipf’s law have relied on city boundaries defined by census data such as metropolitan areas and census-designated places. However, these definitions are often criticized for being subjective or arbitrary. In this paper, an alternative approach is taken to define urban agglomerations through clustering street nodes (intersections and ends), which the authors term “natural cities.” Based on this demarcation method, it was found that Zipf’s law holds remarkably well for all natural cities across the United States, with over 2-4 million such entities identified. The findings show little sensitivity to the clustering resolution used in defining these natural cities. In contrast, urban areas defined by census data do not consistently adhere to Zipf’s law. This research highlights the importance of how city boundaries are delineated and suggests that a more objective method based on street node clustering can provide valuable insights into urban scaling laws.