Under this section, we will look at the various anonymization approaches proposed for undirected weighted social networks alone. The weight on edges can represent degree of friendship, trustworthiness, behaviour, etc. We will consider directed weighted social networks as a different section later. As stated in the introductory chapters, a weighted social network graph is one where the edges between vertices have quantifiable weights associated with them. It is given by where is the set of nodes, is the set of edges and is the matrix of weights associated with the edges such that is the weight in edge that connects nodes and .