k-symmetry model for identity anonymization in social networks

Abstract

With more and more social network data being released, protecting the sensitive information within social networks from leakage has become an important concern of publishers. Adversaries with some background structural knowledge about a target individual can easily re-identify him from the network, even if the identifiers have been replaced by randomized integers(i.e., the network is naively-anonymized). Since there exists numerous topological information that can be used to attack a victim's privacy, to resist such structural re-identification becomes a great challenge. Previous works only investigated a minority of such structural attacks, without considering protecting against re-identification under any potential structural knowledge about a target. To achieve this objective, in this paper we propose -symmetry model, which modifies a naively-anonymized network so that for any vertex in the network, there exist at least − 1 structurally equivalent counterparts. We also propose sampling methods to extract approximate versions of the original network from the anonymized network so that statistical properties of the original network could be evaluated. Extensive experiments show that we can successfully recover a variety of such properties of the original network through aggregations on quite a small number of sample graphs.

Graph Editing to a Given Neighbourhood Degree List is Fixed-Parameter Tractable

“…An example of such a graph measure is degree anonymity [37], which is useful in complex network analysis. In fact, k-degree-anonymity is one of many k-anonymity criteria for privacy preservation in social networks − others include k-neighbourhood-isomorphism [56], where the neighbourhood of any vertex is "similar" to the neighbourhoods of at least k − 1 other vertices, and k-symmetry [54], where each vertex can be mapped to at least k − 1 other vertices by automorphism.…”

Triangle randomization for social network data anonymization

“…• Perturbation based techniques: The original social network is modified by adding and/or removing vertices and/or edges [3,10,19,20,21].…”

“…The kSymmetry [19] and k-Automorphism [20] models aim to protect against "identity disclosure" (vertex anonymity) by adding vertices and edges until, for each vertex of the graph, there exist at least k − 1 other vertices that are structurally equivalent to it. The kIsomorphism [3] model also considers edge privacy and generates an anonymous graph that consists of k disjoint isomorphic subgraphs.…”

Preservation of Structural Properties in Anonymized Social Networks

“…Zou et al assume a more powerful adversary and their model, titled kautomorphism anonymity, requires that each node from the social network is unindistinguisable from other k-1 nodes with respect to any subgraph in which the node belongs [45]. Two other models, named k-symmetry [8] and k-isomorphism [40], are similar to k-automorphism. The social networks that satisfy one of these three models are created via a process of both node-and edge-additions / deletions.…”

“…Other less related works that analyze a limited number of structural properties were performed only for graph modification approaches such as k-isomorphism [8] and ksymmetry [40].…”