The prevalence of social networks has raised the concern for individual privacy leakage. Although preserving user privacy in social networks has been studied extensively, there is still a lot of room for improvement in the state of the art techniques. For example, the recently proposed K-automorphism model can prevent node identity attack by constructing a K-automorphism graph; however, it ignores preserving the privacy of the edges, resulting in path length leakage and edge leakage in the anonymous graph. Another example is the K-isomorphism model, which was proposed to improve the K-automorphism model by transforming the graph of social networks into K disjoined isomorphic subgraphs. However, it cuts off the connection among subgraphs, which impairs the data utility of the released anonymous graph. In this paper, we design a secure and high utility privacy preserving model, called AK-secure, to prevent node identity attack, path length leakage, and edge leakage effectively. On the basis of the AK-secure privacy preserving model, we propose a graph anonymous algorithm, which constructs an anonymous graph satisfying the AK-secure privacy preserving model, minimizing information loss and guaranteeing high data utility. Extensive experiments on real data sets show the security, effectiveness of our AK-secure privacy preserving model and the high data utility of the released anonymous graph. Copyright © 2013 John Wiley & Sons, Ltd.