Suburbanization and the rank-size rule

Abstract

In this article, we revisit Zipf's law and test the rank-size rule on US cities for different periods of time and city limits. We show that Zipf 's law holds more closely for urban places in 1900 and recently, in 1990 and 2000, for metropolitan areas. With the evolution of the modern city, the changes in infrastructure and the cost of commuting that have contributed to an urban spread, the metropolitan area is perhaps representing today's communities better, as urban places did 100 years ago. In that sense, the rank-size rule continues to hold with the appropriate redefinition of a city.

Notes

¹ In addition to city populations, Zipf's law can also be applied to several fields of study. Zipf applied the rank-size rule to the rank and frequency of words in a text. Recent studies have used the works of Shakespeare to illustrate this concept. Studies have also shown that the rank-size rule applies to many languages, such as the study by Ha et al. (2002) which demonstrated that Zipf's law holds for both English and Mandarin. Zipf's law has also recently been applied successfully to the popularity of web sites, measuring the number of hits to a web site and that sites ranking (Adamic, 2002).

² A number of studies include data from the 1990's among them Gabaix (1999) so we include the 1990 data for comparison.