Weighted evolving network with geographical constraints

Complex networks have established themselves as being particularly suitable and flexible for representing and modeling several complex natural and human-made systems. Inspired by studies on airline and shipping networks, we propose a transport network model that includes geographical attributes along with topological and weight properties. In this model we introduce the theory of cost in micro-economics, regard distance between vertices as a function of cost. In general, a long-range connection cost higher and happen to appear rarely based on this, in our model the topological growth and weight dynamics are both determined by geographical distance cost and capacity of dealing with traffic load in a given vertex. Then we analyze some attributes of this model, the results suggest that the interplay between weight dynamics and spatial constraints is a key ingredient in order to understand the underlying driving factor of real-world weighted networks.