In recent years there has been a significant raise in the use of graph-formatted data. For instance, social and healthcare networks present relationships among users, revealing interesting and useful information for researches and other third-parties. Notice that when someone wants to publicly release this information it is necessary to preserve the privacy of users who appear in these networks. Therefore, it is essential to implement an anonymization process in the data in order to preserve users' privacy. Anonymization of graph-based data is a problem which has been widely studied last years and several anonymization methods have been developed. In this chapter we summarize some methods for privacy-preserving on networks, focusing on methods based on the k-anonymity model. We also compare the results of some k-degree anonymous methods on our experimental set up, by evaluating the data utility and the information loss on real networks.