A Scale-Free Network Structure Explains the
City-Size Distribution ∗
Marcus Berliant† and Hiroki Watanabe‡
October 30, 2008
Zipf’s law is one of the most well-known empirical regularities of the
city-size distribution and explaining it has long been the Holy Grail of
urban economics. There is extensive research on the subject, where each
city is treated equally in terms of transactions with other cities. Recent
developments in network theory facilitate the examination of asymmet-
ric communication patterns among the cities. Under the scale-free net-
work framework, the chance of observing extremes becomes lower than
the Gaussian distribution predicts and therefore it explains the emergence
of large clusters. City-size distributions share the same pattern. This paper
proposes a way to incorporate network structure into the urban economics
with a view to explaining the city-size distribution.
Keywords: Zipf’s law, city-size distribution, fractals, self-organizing
economy, Gibrat’s law, random graph, scale-free network.
1.1 Distribution of City Size and Network Theory
Any economic activity is associated with the location where it takes place.
Standard economic theory is sufficient to analyze these activities as long as
they take place at the same location, which is not the case when it comes
to the location choice of consumers or firms. The distribution of city size
is not degenerate in one location nor is it uniform. Your local economy is
not independent of your neighboring economies unless your local economy is
autarkic. A transaction pattern between any two cities alters the way cities are
populated and modifies the overall city-size distribution.
∗This project received a grant from the Center for Research in Economics and Strategy (CRES),
in the Olin Business School, Washington University in St. Louis. The second author thanks Pro-
fessors Sukkoo Kim, Jody O’Sullivan, and Victor Wickerhauser for their helpful comments and
†Department of Economics, Washington University, Campus Box