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Many complex dynamical networks display synchronization phenomena. We introduce a general complex dynamical network model. The model is equivalent to a simple vector model of adopting the Kronecker product. Some synchronization criteria, including time-variant networks and time-varying networks, are deduced based on Lyapunovs stability theory, and they are proven on the condition of obtaining a certain synchronous solution of an isolated cell. In particular, the inner-coupling matrix directly determines the synchronization of the time-invariant network; while for a time-varying periodic dynamical network, the asymptotic stability of a synchronous solution is determined by a constant matrix which is related to the fundamental solution matrices of the linearization system. Finally, illustrative examples are given to validate the results.