The advent of social network sites in the last years seems to be a trend that will likely continue. What naive technology users may not realize is that the information they provide online is stored and may be used for various purposes. Researchers have pointed out for some time the privacy implications of massive data gathering, and effort has been made to protect the data from unauthorized disclosure. However, the data privacy research has mostly targeted traditional data models such as microdata. Recently, social network data has begun to be analyzed from a specific privacy perspective, one that considers, besides the attribute values that characterize the individual entities in the networks, their relationships with other entities. Our main contributions in this paper are a greedy algorithm for anonymizing a social network and a measure that quantifies the information loss in the anonymization process due to edge generalization.