Abstract
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.
Highlights
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 and reflects the notion that highly connected individuals tend to live in highly populated areas
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
Summary
The precise nature of the geographical distribution of human populations and their concurrent network of social contacts has drawn considerable interest in recent years because of its critical role in the spread of epidemics and in developing effective immunization strategies for their arrest [1,2,3,4], and its effect on the evolution of the electoral map during election times, on the spread of rumors and ideas [5], and on commerce, transportation, and city planning [6,7,8,9]. A most recent study addresses the relation between social connectivity and city population, exploiting country-scale mobile communication data [16]
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