Graph comparison and its application in network synchronization

Using the tool of graph comparison from spectral graph theory, we propose new methodologies to guarantee complete synchronization in complex networks. The main idea is to utilize flexibly topological features of a given network so that the eigenvalues of the Laplacian matrix associated with the network can be estimated. The proposed methodologies enable the construction of different coupling-strength combinations in response to different knowledge about sub-networks. The obtained bounds of the network graphs' eigenvalues can be further used to study the robust synchronization problem in face of link failures in networks. Examples are utilized to demonstrate how to apply the methodologies to networks.