Anonymizing Graphs

TL;DR

This paper introduces a new graph anonymization model called (k,l)-anonymity to protect social network privacy, analyzes the computational complexity of achieving it, and provides algorithms for different cases.

Contribution

It defines the (k,l)-anonymity model for graphs, studies the complexity of making graphs satisfy this property, and offers polynomial-time solutions and approximations for various parameters.

Findings

Certain (k,l)-anonymity problems are polynomial-time solvable.

Other cases of the problem are NP-hard.

Approximation algorithms are provided for NP-hard cases.

Abstract

Motivated by recently discovered privacy attacks on social networks, we study the problem of anonymizing the underlying graph of interactions in a social network. We call a graph (k,l)-anonymous if for every node in the graph there exist at least k other nodes that share at least l of its neighbors. We consider two combinatorial problems arising from this notion of anonymity in graphs. More specifically, given an input graph we ask for the minimum number of edges to be added so that the graph becomes (k,l)-anonymous. We define two variants of this minimization problem and study their properties. We show that for certain values of k and l the problems are polynomial-time solvable, while for others they become NP-hard. Approximation algorithms for the latter cases are also given.