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Network embedding is a very important method for network data. However, most of the algorithms can only deal with static networks. In this paper, we propose an algorithm Recurrent Neural Network Embedding (RNNE) to deal with dynamic network, which can be typically divided into two categories: a) topologically evolving graphs whose nodes and edges will increase (decrease) over time; b) temporal graphs whose edges contain time information. In order to handle the changing size of dynamic networks, RNNE adds virtual node, which is not connected to any other nodes, to the networks and replaces it when new node arrives, so that the network size can be unified at different time. On the one hand, RNNE pays attention to the direct links between nodes and the similarity between the neighborhood structures of two nodes, trying to preserve the local and global network structure. On the other hand, RNNE reduces the influence of noise by transferring the previous embedding information. Therefore, RNNE can take into account both static and dynamic characteristics of the network.We evaluate RNNE on five networks and compare with several state-of-the-art algorithms. The results demonstrate that RNNE has advantages over other algorithms in reconstruction, classification and link predictions.