### 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.

Original language | English (US) |
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Title of host publication | Theory of Cryptography - 10th Theory of Cryptography Conference, TCC 2013, Proceedings |

Pages | 457-476 |

Number of pages | 20 |

DOIs | |

State | Published - Feb 21 2013 |

Event | 10th Theory of Cryptography Conference, TCC 2013 - Tokyo, Japan Duration: Mar 3 2013 → Mar 6 2013 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 7785 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 10th Theory of Cryptography Conference, TCC 2013 |
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Country | Japan |

City | Tokyo |

Period | 3/3/13 → 3/6/13 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Theory of Cryptography - 10th Theory of Cryptography Conference, TCC 2013, Proceedings*(pp. 457-476). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7785 LNCS). https://doi.org/10.1007/978-3-642-36594-2_26

}

*Theory of Cryptography - 10th Theory of Cryptography Conference, TCC 2013, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 7785 LNCS, pp. 457-476, 10th Theory of Cryptography Conference, TCC 2013, Tokyo, Japan, 3/3/13. https://doi.org/10.1007/978-3-642-36594-2_26

**Analyzing graphs with node differential privacy.** / Kasiviswanathan, Shiva Prasad; Nissim, Kobbi; Raskhodnikova, Sofya; Smith, Adam Davison.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Analyzing graphs with node differential privacy

AU - Kasiviswanathan, Shiva Prasad

AU - Nissim, Kobbi

AU - Raskhodnikova, Sofya

AU - Smith, Adam Davison

PY - 2013/2/21

Y1 - 2013/2/21

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84873947082&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84873947082&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-36594-2_26

DO - 10.1007/978-3-642-36594-2_26

M3 - Conference contribution

SN - 9783642365935

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 457

EP - 476

BT - Theory of Cryptography - 10th Theory of Cryptography Conference, TCC 2013, Proceedings

ER -