Topological Analysis of Specific Spatial Complex Networks

Based on analyses of specific spatial networks, we compare the accuracy of three models in capturing topologies of two types of spatial networks: electronic circuits and brain networks. The models analyzed are an optimization model trading off multiple-objective constraints, an extended preferential attachment model with spatial constraints, and the generalized random graph model. First, we find that the optimization model and the spatial preferential attachment model can generate similar topological structures under appropriate parameters. Second, our experiments surprisingly show that the simple generalized random graph model outperforms the two proposed models. Third, we find that a series of spatial networks under global optimization of wire length, including the electronic circuits, brain networks, neuronal networks and transportation networks, have high s-metric values close to those of the corresponding generalized random graph models. These s-metric observations explain why the generalized random graph model can match the electronic circuits and the brain networks well from a probabilistic viewpoint, and distinguish their structures from self-organized spatial networks, such as the Internet.