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

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.

Fractal Analysis Based on Hierarchical Scaling in Complex Systems

“…Recently, Bin Jiang and his coworkers have proposed a concept of "natural city" and developed a novel approach to measure objective city sizes based on street nodes or blocks and thus urban boundaries can be naturally identified [18,25]. The street nodes are defined as street intersections and ends, while the naturally defined urban boundaries constitute the region of what is called natural cities.…”

“…Many types of physical and social phenomena satisfy the well-known ranksize distribution and thus follow Zipf's law [7,11,18]. Today, Zipf's law has been used to describe the discrete power law probability distributions in various natural and human systems [3,19].…”

Are We in Boswash Yet? A Multi-Source Geodata Approach to Spatially Delimit Urban Corridors

“…Ref. [48] derive "natural cities" through clustering OpenStreetMap road data, without any census information, aiming to validate Zipf's law for the United States. Ref.…”

Are Cities in Vietnam Distributed According to Zipf?

“…If a minimum "city" size of 12,000 inhabitants and a radius of 3000 meters are chosen, this method produces 1,947 city clusters for the entire US. Jiang and Jia (2011), also noting that cities are usually administratively defined, propose another alternative method. They employ a process to detect clustering based on street nodes (including intersections and ends) to define what they term natural cities for the entire United States.…”