The common approach for implementing social networks has been using centralized infrastructures, which inherently include problems of privacy, censorship, scalability, and fault-tolerance. Although decentralized systems offer a natural solution, significant research is needed to build an end-to-end peer-to-peer social network where data is stored among trusted users. The centralized algorithms need to be revisited for a P2P setting, where the nodes have connectivity to only neighbors, have no information of global topology, and may go offline and churn resulting in changes of the graph structure. The social graph algorithms should be designed as robust to node failures and network changes. We model P2P social networks as uncertain graphs where each node can go offline, and we introduce link recommendation algorithms that support the development of decentralized social networks. We propose methods to recommend top-k links to improve the underlying topology and efficiency of the overlay network, while preserving the locality of the social structure. Our approach aims to optimize the probabilistic reachability, improve the robustness of the local network and avoid loss from failures of the peers. We model the problem through discrete optimization and assign a score to each node to capture both the topological connectivity and the social centrality of the corresponding node. We evaluate the proposed methods with respect to performance and quality measures developed for P2P social networks.