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Connectivity-based node clustering has wide-ranging applications in decentralized peer-to-peer (P2P) networks such as P2P file sharing systems, mobile ad-hoc networks, P2P sensor networks, and so forth. This paper describes a connectivity-based distributed node clustering scheme (CDC). This scheme presents a scalable and efficient solution for discovering connectivity-based clusters in peer networks. In contrast to centralized graph clustering algorithms, the CDC scheme is completely decentralized and it only assumes the knowledge of neighbor nodes instead of requiring a global knowledge of the network (graph) to be available. An important feature of the CDC scheme is its ability to cluster the entire network automatically or to discover clusters around a given set of nodes. To cope with the typical dynamics of P2P networks, we provide mechanisms to allow new nodes to be incorporated into appropriate existing clusters and to gracefully handle the departure of nodes in the clusters. These mechanisms enable the CDC scheme to be extensible and adaptable in the sense that the clustering structure of the network adjusts automatically as nodes join or leave the system. We provide detailed experimental evaluations of the CDC scheme, addressing its effectiveness in discovering good quality clusters and handling the node dynamics. We further study the types of topologies that can benefit best from the connectivity-based distributed clustering algorithms like CDC. Our experiments show that utilizing message-based connectivity structure can considerably reduce the messaging cost and provide better utilization of resources, which in turn improves the quality of service of the applications executing over decentralized peer-to-peer networks.