Instead of improving the network synchronizability, we focus in this paper on investigating the redundant links for synchronization.
The network synchronizability will stay almost unchanged if these links are removed. In order to accurately identify and remove the redundant links, we design a greedy algorithm based on the eigenvector of the Laplacian matrix.
We validate the algorithm by directly comparing the simulation of the Kuramoto model on the original network and the reduced network.
With this algorithm, we find that the homogeneous networks generally have more redundant links than the heterogeneous networks do.