The spatial structure of networks

We study networks that connect points in geographic space, such as transportation networks and the Internet. We find that there are strong signatures in these networks of topography and use patterns, giving the networks shapes that are quite distinct from one another and from non-geographic networks. We offer an explanation of these differences in terms of the costs and benefits of transportation and communication, and give a simple model based on the Monte Carlo optimization of these costs and benefits that reproduces well the qualitative features of the networks studied. PACS. 89.75.Hc Networks and genealogical trees – 87.23.Ge Dynamics of social systems – 05.90.+m Other topics in statistical physics, thermodynamics, and nonlinear dynamical systems – 64.60.Ak Renormalization-group, fractal, and percolation studies of phase transitions