A new concept dafincd as k-weak minimal cut set, which, is used to characterize the weakness of the weak link set, is established in this paper. Based on this concept, a fast algcrithm or searching k-weak minimal cut set in large scale networks is proposed. From the analysis of computation complexity, it is shown that the frequency count of the algorithm is much lower and the algorithm is powerful to adequacy evaluation of the transmission capacity in large scale networks.