Growing highly synchronizable scale-free networks

In this letter, a model for growing highly synchronizable networks is introduced. The model is based on preferential attachment in which the new nodes tip to old ones in a way to maximize the synchronization properties of the network. Criteria based on the eigenvectors corresponding to the second smallest and the largest eigenvalues of the Laplacian matrix of the connection graph were used to choose the old nodes to which a new node makes connection. Numerical simulations showed that these networks have considerably lower eigenratio (the largest eigenvalue of the Laplacian divided by the second smallest one), and hence better synchronizability, as compared to standard Barab´asi-Albert (BA) scale-free networks. These two models were also different in their statistical properties. BA networks demonstrated larger global and local efficiency, while modularity and assortativity of highly synchronizable networks were larger. The proposed model resulted in networks with almost power-law degree distribution (except an exponential start). Furthermore, the hub nodes in these networks had much smaller degree as compared to those of BA networks.