Complexity and Optimization Analysis of Spatial Network

Abstract

Optimization is a classical problem in graph theory, and lots of researchers are working on the complexity of complex networks. We visualize and analyze some countriespsila national highway networks with Pajek and Ucinet, and find that they share several universal topological properties: tending to choose short edges, average degree is smaller than 4, small clustering coefficient and large diameter, and the degree distribution can be expressed in a general formula. All of above characteristics attribute to 2-dimension of the spatial network. Then we modify the optimization model from the economic viewpoint and use genetic algorithm to optimize the networks, which is proved useful and effective.