  We propose a bare-bones stochastic model that takes into account both the
geographical distribution of people within a country and their complex network
of connections. The model, which is designed to give rise to a scale-free
network of social connections and to visually resemble the geographical spread
seen in satellite pictures of the Earth at night, gives rise to a power-law
distribution for the ranking of cities by population size (but for the largest
cities) and reflects the notion that highly connected individuals tend to live
in highly populated areas. It also yields some interesting insights regarding
Gibrat's law for the rates of city growth (by population size), in partial
support of the findings in a recent analysis of real data [Rozenfeld et al.,
Proc. Natl. Acad. Sci. U.S.A. 105, 18702 (2008)]. The model produces a
nontrivial relation between city population and city population density and a
superlinear relationship between social connectivity and city population, both
of which seem quite in line with real data.
