Spatially distributed social complex networks

TL;DR

This paper introduces a simple stochastic model that captures the geographical and social network structures of cities, reproducing key empirical patterns like scale-free distributions and superlinear connectivity growth.

Contribution

The model integrates geographical distribution and social connections to replicate real-world urban and social network patterns, providing new insights into city growth and connectivity.

Findings

Reproduces scale-free city size distribution.

Shows superlinear growth of social connections with city size.

Aligns with empirical data on city density and growth laws.

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.