The transmission-network reconfiguration is the second step of power system restoration after a complete blackout or a local outage. The most important issues in this step are to determine the optimal skeleton-network for reconfiguration and to optimize the sequence of restoration paths. Based on the weighted complex network model， a new transmission-network reconfiguration method is presented. The generation capacity of non-black-start generators and that of the important loads， as well as the distribution and importance degree of each bus， are taken into account in the proposed method. The weighted edge betweenness， which reflects the importance of each edge in the network interconnection， is employed to direct the optimization of restoration paths， and the global optimal sequence of restoration paths could then be obtained. The optimal skeleton-network in which important generation and load buses are included could also be obtained. Hence， the problem associated with the existing methods in which the restoration paths and the skeleton-network are separately optimized could then be solved at least to some extent by using the proposed method. The shortcomings of the existing methods for optimizing restoration paths based on the experience of experts or the section-searching strategy could be overcome. Finally， the New England 10-unit 39-bus system is employed to illustrate the essential features of the proposed method.