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A large amount of valuable information resides in decentralized social graphs, where no entity has access to the complete graph structure. Instead, each user maintains locally a limited view of the graph. For example, in a phone network, each user keeps a contact list locally in her phone, and does not have access to other users' contacts. The contact lists of all users form an implicit social graph that could be very useful to study the interaction patterns among different populations. However, due to privacy concerns, one could not simply collect the unfettered local views from users and reconstruct a decentralized social network.

In this paper, we investigate techniques to ensure local differential privacy of individuals while collecting structural information and generating representative synthetic social graphs. We show that existing local differential privacy and synthetic graph generation techniques are insufficient for …