Publishing Number of Walks and Katz Centrality under Local Differential Privacy

Louis BETZER, Vorapong Suppakitpaisarn, Quentin Hillebrand

Keywords: AI under privacy constraints, local differential privacy, social network analysis and graph algorithms, Katz centrality

TL;DR: In our study, we present an algorithm for publishing the count of walks and Katz centrality under local differential privacy (LDP), complemented by a comprehensive theoretical analysis.

Abstract: In our study, we present an algorithm for publishing the count of walks and Katz centrality under local differential privacy (LDP), complemented by a comprehensive theoretical analysis. While previous research in LDP has predominantly focused on counting subgraphs with a maximum of five nodes, our work extends this to larger subgraphs. The primary challenge in such an extension lies in managing the exponentially increasing noise associated with LDP as the size of the subgraph grows. Our solution involves an algorithm for publishing the count of walks originating from each node in the graph, which subsequently enables us to publish the Katz centrality of all nodes. This algorithm incorporates multiple communication rounds and employs a clipping technique. Through both theoretical and empirical evaluation, we demonstrate that our algorithm achieves has a relatively small bias and variance, showing significant improvements over both the randomized response method and non-clipping algorithms. Additionally, our approach to estimating Katz centrality successfully identifies up to 90\% of the nodes with the highest centrality values.

List Of Authors: Betzer, Louis and Suppakitpaisarn, Vorapong and Hillebrand, Quentin

Code Url: https://github.com/louisbetzer/Katz-Centrality-Local-Differential-Privacy

Video Url: https://www.youtube.com/watch?v=CglDgS4fRYA

Submission Number: 141