The proliferation of social networks, where individuals share private information, has caused, in the last few years, a growth in the volume of sensitive data being stored in these networks. As users subscribe to more services and connect more with their friends, families, and colleagues, the desire to use this information from the networks has increased. Online social interaction has become very popular around the globe and most sociologists agree that this will not fade away. Social network sites gather confidential information from their users (for instance, the social network site PacientsLikeMe collects confidential health information) and, as a result, social network data has begun to be analyzed from a different, specific privacy perspective. Since the individual entities in social networks, besides the attribute values that characterize them, also have relationships with other entities, the risk of disclosure increases. In this talk we present a greedy algorithm for anonymizing a social network and a measure that quantifies the information loss in the anonymization process due to edge generalization.