On Enhancing Synchronization Properties of Dynamical Networks Using Node and Edge Centrality Measures

In this paper a method for enhancing the synchronizability of dynamical networks is discussed. The method considers both local structural properties, i.e. node degrees, and global properties, i.e. node and edge betweenness centrality measures. Its performance is compared with that of some other heuristic methods and the evidence for its superior behavior is discussed. As an index for the synchronizability of a dynamical network, the eigenratio of the Laplacian matrix of the connection graph is considered. As network structures, scale-free, Watts-Strogatz and random networks of different sizes and topological properties are used. Numerical calculations of the eigenratio in the networks weighted through different methods support the conclusion.