Searching good indicators for predicting the synchronizability of heterogeneous networks and beyondL. Chen1, H. B. Huang1, G. X. Qi1, 2, P. Luo1, C. Qiu1, X. D. Zhao1 and Y. Wang1
1 Department of Physics, Southeast University - Nanjing 210096, China
2 Institute of Neurosciences and Biophysics INB-3, Research Center Jülich - Jülich 52425, Germany
received 18 April 2008; accepted in final form 21 October 2008; published December 2008
published online 2 December 2008
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.
05.45.Xt - Synchronization; coupled oscillators.
89.75.Hc - Networks and genealogical trees.
© EPLA 2008