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Recently, it has been demonstrated that many large complex networks display a scale-free feature, that is, their connectivity distributions are in the power-law form. In this paper, we investigate the synchronization phenomenon in scale-free dynamical networks. We show that if the coupling strength of a scale-free dynamical network is greater than a positive threshold, then the network will synchronize no matter how large it is. We show that the synchronizability of a scale-free dynamical network is robust against random removal of nodes, but is fragile to specific removal of the most highly connected nodes.
Wang et al. (Tue,) studied this question.