Publishing Social Network Graph Eigenspectrum With Privacy Guarantees

Online social networks (OSNs) often refuse to publish their social network graphs due to privacy concerns. Recently, differential privacy has become the widely accepted criteria for privacy preserving data publishing. Although some work has been done on publishing matrices with differential privacy, they are computationally unpractical as they are not designed to handle large matrices such as adjacency matrices of OSN graphs. In this paper, we propose a random matrix approach to OSN data publishing, which achieves storage and computational efficiency by reducing dimensions of adjacency matrices and achieves differential privacy by adding a small amount of noise. Our key idea is to first project each row of an adjacency matrix into a low-dimensional space using random projection, and then perturb the projected matrix with random noise, and finally publish the perturbed and projected matrix. In this paper, we first prove that random projection plus random perturbation preserve differential privacy, and also that the random noise required to achieve differential privacy is small. We validate the proposed approach and evaluate the utility of the published data for three different applications, namely node clustering, node ranking, and node classification, using publicly available OSN graphs of Facebook, LiveJournal, and Pokec.

I. Introduction

ONLINE Social Networks (OSNs) have become an essential part of modern life. Billions of users connect and share information using OSNs such as Facebook and Twitter. Graphs obtained from these OSNs can provide useful insights on various fundamental societal phenomena such as epidemiology, information dissemination, marketing, and sentiment flow [2], [12], [23], [55], [56]. Various analysis methods [8], [13], [22], [37], [40] have been applied to OSNs by explicitly exploring its graph structure, such as clustering analysis for automatically identifying online communities and node influence analysis for recognizing the influential nodes in social networks. The basis of all these analysis is to represent a social network graph by an adjacency matrix and then represent individual nodes by vectors derived from the top eigenvectors of the adjacency matrix. Thus, all these analysis methods require real social network graphs.