Zipf's Law for Cities
A quick glance at the list of the most populous cities in the United States reveals a very interesting, though apparently random trend. The most populous city, New York City (population 8.5 million ), has approximately twice the population of the second most populous city (Los Angeles, population 4 million), three times the population of the third most populous city (Chicago, 2.7 million), and four/five times the populations of the fourth/fifth most populous cities (Houston, 2.1 million, and Philadelphia, 1.5 million). This trend in frequency vs. rank continues for nearly all “mega-cities” (population centers of over 100,000 people) in the United States.
This phenomenon is commonly referred to as Zipf’s Law, after linguist George Zipf.