There are two main mechnisms for preserving link privacy between labeled vertices. The first approach is to perform clustering of vertices and edges,and aggregate them into super vertices.in this way,information about corresponding sub-graphs can be anonymized.While these clustering approaches permit analysis of some macro-level graph properties,they are not suitable for blackbox application of existing social network based applications.such as sybil defenses.The second class of approaches aim to introduce perturbation in the social graph by adding and deleting edges and vertices.Next ,we discuss this line of research in more detail.
Hay propose a perturbation algorithm which applies a sequences of K edge deletions followed by k random edge insertions.Candidates for edge deletion are sampled uniformly at random from the space of existing edges in graph G,while candidates for edge insertion are sampled uniformly at random from the space of edges not in G.The key difference between our perturbation mechanism and that of Hay is that we sample edges for insetion based on the structure of the original graph(as opposed to random selection).