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Due to the complexity of cascading failures and blackouts, the small world theory for complex network research is employed in probing the mechanism of them. In the paper, the original small world network model has been modified in two ways. Firstly, the magnitude of the line impedance regarded as the weight of edges is taken into consideration which is not considered in the original model. The formulae of corresponding parameters of the model are also modified. The calculation results of some practical grids validate the correctness and effectiveness of the new model. Secondly, the complex number format of power flow is introduced as the network flow in the small world model. With the power flow and the topology of grids, the two main factors to the system vulnerability, considered, the improved small world model can be used as a tool for vulnerability analysis of grids.