Scaling properties in spatial networks and their effects on topology and traffic dynamics

Empirical studies on the spatial structures in several real transport networks reveal that the distance distribution in these networks obeys a power law. To discuss the influence of the power law exponent on the network's structure and function, a spatial-network model is proposed. Based on a regular network and subject to a limited cost C, long-range connections are added with power law distance distribution P(r) = ar-δ. Some basic topological properties of the networks generated by the model with different δ are studied. It is found that the network has the smallest average shortest path when δ = 2. Then a classic traffic model on our model networks is investigated. It is found that δ = 1.5 is the optimization value for the traffic process in our model. All of these results give us some deep understanding about the relationship between spatial structure and network function