Edge Selection for Degree Anonymization on K Shortest Paths

Abstract

Privacy preserving network publishing has been studied extensively in recent years. Although more works have adopted un-weighted graphs to model network relationships, weighted graph modeling can provide deeper analysis of the degree of relationships. Previous works on weighted graph privacy have concentrated on preserving the shortest path characteristic between pairs of vertices. Two common types of privacy have been proposed. One type of privacy tried to add random noise edge weights to the graph but still maintain the same shortest path. The other privacy, k-shortest path privacy, minimally perturbed edge weights so that there exist k shortest paths. However, the k-shortest path privacy did not consider degree attacks on the nodes of anonymized shortest paths. For example, if the adversary possesses background knowledge of node degrees on the shortest path, the true shortest path can be identified. We have previously presented a new concept called (k ₁ , k ₂ )-shortest path privacy to prevent such privacy breach [1]. A published network graph with (k ₁ , k ₂ )-shortest path privacy has at least k ₁ indistinguishable shortest paths between the source and destination vertices. In addition, for the non-overlapping vertices on the k ₁ shortest paths, there exist at least k ₂ vertices with same node degree and lie on more than one shortest path. In this work, we further propose edge insertion and edge weight determination techniques to effectively achieve the proposed privacy. Numerical comparisons based on average clustering coefficient and average shortest path length show that the proposed TNF approach is simple and effective.