Optimization of spatial complex networks

Abstract

First, we estimate the connectivity properties of a predefined (fixed node locations) spatial network which optimizes a connectivity functional that balances construction and transportation costs. In this case we obtain a Gaussian distribution for the connectivity. However, when we consider these spatial networks in a growing process, we obtain a power law distribution for the connectivity. If the transportation costs in the functional involve the shortest geometrical path, we obtain a scaling exponent $\gamma =2.5$. However, if the transportation costs in the functional involve just the shortest path, we obtain $\gamma =2.2$. Both cases may be useful to analyze in some real networks.