Private Analysis of Graph Structure

Abstract

We present efficient algorithms for releasing useful statistics about graph data while providing rigorous privacy guarantees. Our algorithms work on data sets that consist of relationships between individuals, such as social ties or email communication. The algorithms satisfy edge differential privacy, which essentially requires that the presence or absence of any particular relationship be hidden.Our algorithms output approximate answers to subgraph counting queries. Given a query graph H, e.g., a triangle, k-star or k-triangle, the goal is to return the number of edgeinduced isomorphic copies of H in the input graph. The special case of triangles was considered by Nissim, Raskhodnikova and Smith (STOC 2007), and a more general investigation of arbitrary query graphs was initiated by Rastogi, Hay, Miklau and Suciu (PODS 2009). We extend the approach of [NRS] to a new class of statistics, namely, k-star queries. We also give algorithms for k-triangle queries using a different approach, based on the higher-order local sensitivity. For the specific graph statistics we consider (i.e., kstars and k-triangles), we significantly improve on the work of [RHMS]: our algorithms satisfy a stronger notion of privacy, which does not rely on the adversary having a particular prior distribution on the data, and add less noise to the answers before releasing them.We evaluate the accuracy of our algorithms both theoretically and empirically, using a variety of real and synthetic data sets. We give explicit, simple conditions under which these algorithms add a small amount of noise. We also provide the average-case analysis in the Erdős-Rényi-Gilbert G(n, p) random graph model.Finally, we give hardness results indicating that the approach NRS used for triangles cannot easily be extended to k-triangles (and hence justifying our development of a new algorithmic approach).

Shortest Paths and Distances with Differential Privacy

“…The two main models which have been considered for applying differential privacy to network structured data are edge and node differential privacy [HLMJ09,BBDS13,KNRS13,KRSY11]. Under edge differential privacy, two graphs are considered to be neighbors if one graph can be obtained from the other by adding or removing a single edge.…”

Publishing Attributed Social Graphs with Formal Privacy Guarantees

“…Fortunately, real-world graphs typically do not contain such pathological structures, and tend to have local sensitivities that are much lower. Triangle counting has been extensively studied in the context of differential privacy (e.g., [25,37,13,5]). The most effective approaches take advantage of the above observation in some way to reduce the amount of noise required to satisfy differential privacy.…”

“…Request permissions from permissions@acm.org. degree distribution [11], subgraph counting [13,2], clustering coefficient [35], and frequent subgraph mining [33]; and (2) private graph release, which typically involves (privately) fitting a generative graph model to input graphs in order to sample a synthetic graph, which can be used in analyses as a proxy for a real input graph (e.g., [23,30,34,4,36,18,29]). We follow this latter approach.…”

Privacy-Preserving Data Publishing in the Cloud: A Multi-level Utility Controlled Approach

“…Based on the concept of differential privacy introduced in [21], there had been many work focused on publishing aggregates of sensitive datasets through differential privacy constraints [23], [3], [7]. Differential privacy had also been applied to protecting sensitive information in graph datasets such that the released information does not reveal the presence of a sensitive element [12], [13], [18]. Recent work had focused on publishing graph datasets through differential privacy constraints so that the published graph maintains as much structural properties as possible as the original graph while providing the required privacy [16].…”