Evolution Dynamic Behavior of Weighted Networks with Disadvantaged Long-Range Connection

Complex networks have established themselves as being particularly suitable and flexible for representing and modeling several complex natural and society systems. In this paper, a model for the growth of weighted networks that couples the establishment of new edges and vertices and weights' dynamical evolution was proposed by analyzing the disadvantaged long-range connection behavior in weighted networks. In the model, we introduced the concepts of field strength and interaction-force in classic charge field theory to construct a simple field theory in networks. Based on interactive-force-driven network evolution dynamics, the model integrates the strength, topology, and distance. In order to present the networks generated by the model, a method to construct weighted networks on lattices was suggested. The networks generated by the model on lattices exhibit the statistical properties observed in several real-world systems. In particular, the model yields the spatial collectivization phenomenon, small world property, and scale-free behavior simultaneously.