Synchronizability and Graph Invariants

Abstract

A huge application in real problems ustifies the enormous interest in the study of the network complexity. A first objective of the research on complex networks is to understand how its structure is affected by the dynamics in progress on them. For instance, it is important to know how the flow of a city traffic, the spread of an epidemic, the blogs growth in the network community and many others is influenced by the network structure. In previous works we studied the synchronizability of a network in terms of the local dynamics [1], [2], assuming that the topology of the graph is fixed. In this paper we are interested in studying the effects of the network structure, i.e., the topology of the graph, in the synchronizability of the network, through the study of some graph parameters, such as the conductance, the clustering coefficient, the performance of the graph and the eigenratio. We define the clustering turning point to identify the formation of clusters and observe its effect on the network synchronization.