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Many real-world social networks are decentralized in nature, and the only way to analyze such a network is to collect local views of the social graph from individual participants. Since local views may contain sensitive information, it is often desirable to apply differential privacy in the data collection process, which provides strong and rigorous privacy guarantees. In many practical situations, the local view of a participant contains not only her own connections, but also those of her neighbors, which are private and sensitive for the neighbors, but not directly so for the participant herself. We call such information beyond direct connections an extended local view (ELV), and study two fundamental problems related to ELVs: first, how do we correctly enforce differential privacy for all participants in the presence of ELVs? Second, how can the data collector utilize ELVs to obtain accurate estimates of global graph properties …