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A small-world network model with preferential attachment is constructed, based on which the effects of various factors such as the characteristic path length, degree distribution, clustering coefficient and betweenness on the synchronizability of complex networks are investigated. It is found that networks with equal characteristic path length and clustering coefficient can still have very different synchronizability. Simulation results show that neither the characteristic path length nor the clustering coefficient of complex networks can solely determines the synchronizability of complex networks, the heterogeneity of the degree distribution essentially suppresses the synchronizability of complex networks, and the maximal betweenness is a reasonable indicator for synchronizability.