Zipf's Law for All the Natural Cities in the United States: A Geospatial Perspective

TL;DR

This study demonstrates that Zipf's law accurately describes the distribution of all natural cities in the U.S., using a novel clustering method that avoids subjective city boundary definitions.

Contribution

The paper introduces a new geospatial approach to defining cities through street node clustering, showing Zipf's law applies broadly to natural cities across the U.S.

Findings

Zipf's law holds for all natural cities in the U.S.

Natural city boundaries are stable across different clustering resolutions.

Census-based city definitions do not consistently follow Zipf's law.

Abstract

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