  While symmetry has been exploited to analyze synchronization patterns in
complex networks, the identification of symmetries in large-size network
remains as a challenge. We present in the present work a new method, namely the
method of eigenvector-based analysis, to identify symmetries in general complex
networks and, incorporating the method of eigenvalue analysis, investigate the
formation and transition of synchronization patterns. The efficiency of the
proposed method is validated by both artificial and empirical network models
consisting of coupled chaotic oscillators. Furthermore, we generalize the
method to networks of weighted couplings in which no strict symmetry exists but
synchronization clusters are still well organized, with the predications
agreeing with the results of direct simulations. Our study provides a new
approach for identifying network symmetries, and paves a way to the
investigation of synchronization patterns in large-size complex network.
