Phil. Trans. R. Soc. A (2009) 367, 3321–3329 doi:10.1098/rsta.2009.0089 Understanding spatial connectivity of individuals with non-uniform population density BY PU WANG 1,2 AND MARTA C. GONZÁLEZ 1, * 1 Center for Complex Network Research, Department of Physics, Biology and Computer Science, Northeastern University, Boston, MA 02115, USA 2 Center for Complex Network Research and Department of Physics, University of Notre Dame, Notre Dame, IN 46556, USA We construct a two-dimensional geometric graph connecting individuals placed in space within a given contact distance. The individuals are distributed using a measured country’s density of population. We observe that while large clusters (group of individuals connected) emerge within some regions, they are trapped in detached urban areas owing to the low population density of the regions bordering them. To understand the emergence of a giant cluster that connects the entire population, we compare the empirical geometric graph with the one generated by placing the same number of individuals randomly in space. We find that, for small contact distances, the empirical distribution of population dominates the growth of connected components, but no critical percolation transition is observed in contrast to the graph generated by a random distribution of population. Our results show that contact distances from real-world situations as for WIFI and Bluetooth connections drop in a zone where a fully connected cluster is not observed, hinting that human mobility must play a crucial role in contact-based diseases and wireless viruses’ large-scale spreading. Keywords: hierarchical geometric graph; random geometric graph; population distribution; continuum percolation; percolation threshold; spatial networks 1. Introduction For humans, population density is the number of people per unit area. Commonly, this may be calculated for a city, a country or the entire world. City population density is, however, heavily dependent on the definition of ‘urban area’ used: densities are often higher for the central municipality itself, compared with the more recently developed and administratively unincorporated suburban communities (http://en.wikipedia.org/wiki/population_density). Mobile phones provide the unique opportunity to estimate the distribution of population density with a spatial resolution never reached previously. By estimating the area of coverage of each mobile phone tower, we can measure the occupation of these areas, and estimate accurately the heterogeneous distribution of population *Author for correspondence (marta.gonzalez.v@gmail.com). One contribution of 14 to a Theme Issue ‘Topics on non-equilibrium statistical mechanics and nonlinear physics’. This journal is © 2009 The Royal Society 3321