Searching good indicators for predicting the synchronizability of heterogeneous networks and beyond

¹  Department of Physics, Southeast University - Nanjing 210096, China
²  Institute of Neurosciences and Biophysics INB-3, Research Center Jülich - Jülich 52425, Germany

Corresponding author: hongbinh@seu.edu.cn

Received: 18 April 2008
Accepted: 21 October 2008

Abstract

In searching the indicators of synchronizability of complex networks, the maximal betweenness centrality is usually proposed as a good indicator. However, we find that a better indicator for synchronizability in heterogeneous networks is the maximal degree from both the average results and the individual realization of a network, which usually makes more sense in practice. Both the largest eigenvalue and the eigenratio are found, in a wide range of heterogeneity, to hold linear relations with the maximal degree. Our results may provide some clues to mathematically solve the relation between the synchronizability and the network degree, also to the optimal strategies to enhance synchronization.