Shortest Paths Publishing With Differential Privacy

The growing prevalence of graphs representations in our society has led to a corresponding rise in the publishing of graphs by researchers and organizations. To protect the privacy, it is important to ensure that graphs including sensitive data are not disclosed. Since the weight of edges could be utilized to infer confidential information, the graph should be privately published to avoid ethical and legal issues. In this paper, we propose a novel method for privately publishing shortest paths while preserving the privacy of sensitive edge weights in graph. Specifically, we divide the edge weights into internal and external edges based on their edge betweenness centrality. Then, we give two different differentially private algorithms to perturb edge weights based on the distinction between internal and external edges, respectively. To reduce the error ratios between differentially private shortest paths and real shortest paths, we employ edge betweenness centrality to search for the shortest path, which is closest to the true one. Our experimental results show that our mechanisms can effectively reduce the error in the average shortest path distance by 1.1% for large graphs, while for the shortest path change rate, our mechanisms can reduce it by 8.3%.