Our work is on outsourcing privacy-preserving social networks to a cloud environment. Research in this area is still in its infancy. To the best of our knowledge, the work is the first to address this problem. The work that is closest to our work can be found in publishing privacy-preserving social networks. As a pioneering work, discussed two re-identification attacks in naive anonymized social networks. In active attacks, an attacker intentionally embeds a subgraph into a social network before publishing and uses such kinds of background knowledge to re-identify nodes and edges in the published network. In passive attacks, an attacker with the knowledge of a target’s subgraph can infer the identity of nodes in the published network. They do not provide a solution to counter these attacks. To defend the re-identification attacks, the work in advocated the k-anonymity model, where every node should be indistinguishable with at least k other nodes in terms of both the attributes and the associated structural information, such as neighborhood and node degree. To preserve the scale and the local structures of the original graph, existing anonymization approaches try to locally modify the graph structure to achieve the privacy preservation requirement. We group nodes by using the following metric: number of one-hop neighbors, in-degree sequence, out-degree sequence, total number of edges, and betweenness. Although other metrics, e.g., closeness centrality and local clustering coefficient, also can be used for grouping, we only consider the above metrics. The concepts of “number of one-hop neighbors” and “total number of edges” are easily understood. They only provide the definitions for the other metrics.
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