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This paper is on the design problem of global exponential adaptive synchronization for a class of stochastic complex dynamical networks. In the considered networks, the dynamics of each node are approximated by a neutral-type neural network. The stochastic disturbances are described in terms of Brownian motions. Different from the prior references, the coefficient matrix of the adaptive controller under consideration is an arbitrary matrix instead of an identity one. By using Lyapunov method and some properties of Kronecker product, a sufficient condition is proposed to ensure the dynamics of the considered network globally exponentially synchronize with the desired solution in the mean square sense. Some criteria for global exponential adaptive synchronization of complex dynamical networks with general nodes are further provided in forms of corollaries. In particular, the proposed criteria for network synchronization are in terms of linear matrix inequalities. Only two variables are used in each criterion and the variables are not inside of any Kronecker product. Hence, the conditions are easy to check. A numerical example is presented to show the effectiveness and applicability of the proposed approach.