Topological structure of peer-to-peer (P2P) networks affects their operating performance. Thus, various models have been proposed to construct an efficient topology for the P2P networks. However, due to the simultaneous failures of peers and other disastrous events, it is difficult to maintain the originally designed topological structure that provides the network with some performance benefits. For this reason, in this paper we propose a simple local rewiring method that changes the network topology to have small diameter as well as highly clustered structure. Moreover, the presented evaluation study shows how these topological properties are involved with the performance of P2P networks.