The City as a Giant Component:  A Random Graph Approach to Zipf's Law

By Raja Kali

 

The emergence of a "city" out of a set of locations in space can be considered akin to the evolution of a random graph.  Interaction between individuals who are connected to each other is at the source of the benefits associated with a city.  If the interaction probability rises, a threshold is eventually crossed at which point most of the graph becomes connected, giving rise to a grand component.  It is at this point that a viable "city" emerges.  This view suggests an interpretation of Zipf's law, which we test using U.S. Census data.