Privacy preserving analysis of a social network aims at a better understanding of the network and its behavior, while at the same time protecting the privacy of its individuals. We propose an anonymization method for weighted graphs, i.e., for social networks where the strengths of links are important. This is in contrast with many previous studies which only consider unweighted graphs. Weights can be essential for social network analysis, but they pose new challenges to privacy preserving network analysis. In this paper, we mainly consider prevention of identity disclosure, but we also touch on edge and edge weight disclosure in weighted graphs. We propose a method that provides k-anonymity of nodes against attacks where the adversary has information about the structure of the network, including its edge weights. The method is efficient, and it has been evaluated in terms of privacy and utility on real word datasets.