Optimization of synchronizability in complex spatial networks

Many real-world phenomena can be modelled as spatial networks where nodes have distinct geographical location. Examples include power grids, transportation networks and the Internet. This paper focuses on optimizing the synchronizability of spatial networks. We consider the eigenratio of the Laplacian Matrix of the connection graph as a metric measuring the synchronizability of the network and develop an efficient rewiring mechanism to optimize the topology of the network for synchronizability, i.e., minimizing the eigenratio. The Euclidean distance between two connected nodes is considered as their connection weights, and the sum of all connection weights is defined as the network cost. The proposed optimization algorithm constructs spatial networks with a certain number of nodes and a predefined network cost. We also study the topological properties of the optimized networks. This algorithm can be used to construct spatial networks with optimal synchronization properties.