Analyzing Graphs with Node Differential Privacy

  • Shiva Prasad Kasiviswanathan
  • Kobbi Nissim
  • Sofya Raskhodnikova
  • Adam Smith
Conference paper

DOI: 10.1007/978-3-642-36594-2_26

Part of the Lecture Notes in Computer Science book series (LNCS, volume 7785)
Cite this paper as:
Kasiviswanathan S.P., Nissim K., Raskhodnikova S., Smith A. (2013) Analyzing Graphs with Node Differential Privacy. In: Sahai A. (eds) Theory of Cryptography. Lecture Notes in Computer Science, vol 7785. Springer, Berlin, Heidelberg

Abstract

We develop algorithms for the private analysis of network data that provide accurate analysis of realistic networks while satisfying stronger privacy guarantees than those of previous work. We present several techniques for designing node differentially private algorithms, that is, algorithms whose output distribution does not change significantly when a node and all its adjacent edges are added to a graph. We also develop methodology for analyzing the accuracy of such algorithms on realistic networks.

The main idea behind our techniques is to “project” (in one of several senses) the input graph onto the set of graphs with maximum degree below a certain threshold. We design projection operators, tailored to specific statistics that have low sensitivity and preserve information about the original statistic. These operators can be viewed as giving a fractional (low-degree) graph that is a solution to an optimization problem described as a maximum flow instance, linear program, or convex program. In addition, we derive a generic, efficient reduction that allows us to apply any differentially private algorithm for bounded-degree graphs to an arbitrary graph. This reduction is based on analyzing the smooth sensitivity of the “naive” truncation that simply discards nodes of high degree.

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Copyright information

© International Association for Cryptologic Research 2013

Authors and Affiliations

  • Shiva Prasad Kasiviswanathan
    • 1
  • Kobbi Nissim
    • 2
  • Sofya Raskhodnikova
    • 3
  • Adam Smith
    • 3
  1. 1.General Electric Global ResearchUSA
  2. 2.Ben-Gurion UniversityIsrael
  3. 3.Pennsylvania State UniversityUSA

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