Abstract
Many real world phenomena can be naturally modeled as graph structures whose nodes representing entities and whose edges representing interactions or relationships between entities. The analysis of the graph data have many practical implications. However, the release of the data often poses considerable privacy risk to the individuals involved. In this paper, we address the edge privacy problem in graphs. In particular, we explore random perturbation for privacy preservation in graph data, and propose an iterative derivation process to analyze node reachability within the graph. We specifically focus on deriving the probability that the shortest path linking two nodes in a directed graph is of a particular length. This allows us to determine the expected length of the shortest path between two nodes, and determine whether they are linked or not. The performance of the proposed method is demonstrated via extensive experiments on both real and synthetic datasets.