In this paper, we study the problem of early detection of fake user accounts on social networks based solely on their network connectivity with other users. Removing such accounts is a core task for maintaining the integrity of social networks, and early detection helps to reduce the harm that such accounts inflict. However, new fake accounts are notoriously difficult to detect via graph-based algorithms, as their small number of connections are unlikely to reflect a significant structural difference from those of new real accounts. We present the SybilEdge algorithm, which determines whether a new user is a fake account (‘sybil’) by aggregating over (I) her choices of friend request targets and (II) these targets’ respective responses. SybilEdge performs this aggregation giving more weight to a user’s choices of targets to the extent that these targets are preferred by other fakes versus real users, and also to the extent that these targets respond differently to fakes versus real users. We show that SybilEdge rapidly detects new fake users at scale on the Facebook network and outperforms state-of-the-art algorithms. We also show that SybilEdge is robust to label noise in the training data, to different prevalences of fake accounts in the network, and to several different ways fakes can select targets for their friend requests. To our knowledge, this is the first time a graph-based algorithm has been shown to achieve high performance (AUC > 0.9) on new users who have only sent a small number of friend requests.