Enhancing the synchronizability of scale-free networks by adding edges

To efficiently enhance the synchronizability of a scale-free network by adding some edges, we numerically study the effect of edge-adding on the spectrum of the network Laplacian matrix. Based on the relation between the largest eigenvalue of the Laplacian matrix and the largest degree of the scale-free network, we show that adding a new edge to the node of largest degree will generally weaken the synchronizability of a scale-free network. We consequently propose a method to effectively enhance the network synchronizability by attaching the new edge to a node whose nearest-neighbors have small degrees. The effect of the new method is analyzed and demonstrated with comparisons. © 2010 World Scientific Publishing Company.