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Privacy in social network data publishing is always an important concern. Nowadays most prior privacy protection techniques focus on static social networks. However, there are additional privacy disclosures in dynamic social networks due to the sequential publications. In this paper, we first show that the risks of vertex and community re-identification exist in a dynamic social network, even if the release at each time instance is protected by a static anonymity scheme. To prevent vertex and community re-identification in a dynamic social network, we propose novel dynamic kw-structural diversity anonymity, where w is the time that an adversary can monitor a victim. This scheme extends the k-structural diversity anonymity to a dynamic scenario. We also present a heuristic to anonymize the releases of networks to satisfy the proposed privacy scheme. The evaluations show that our approach can retain much of the characteristics of the networks while confirming the privacy protection.