The Empirical study indicates that the anonymized social networks

Social networks have developed rapidly, recent research has begun to explore social networks to understand their structure, advertising and marketing, and data mining. Cloud computing as an emerging computing paradigm, is expected to reshape the information technology processes in the near future. Cloud services, which are available in a payas- you-go manner, promise ubiquitous 24/7 access at a low cost. Due to the overwhelming merits of cloud computing, e.g., flexibility and scalability, more and more organizations that host social network data choose to outsource a portion of their data to a cloud environment . Preserving privacy when publishing social network data becomes an important issue. Social networks model social relationships with a graph structure using nodes and edges, where nodes model individual social actors in a network, and edges model relationships between social actors . The relationships between social actors are often private, and directly outsourcing the social networks to a cloud may result in unacceptable disclosures. For example, publishing social network data that describes a set of social actors related by sexual contacts or shared drug injections may compromise the privacy of the social neighborhood attacks in a social network. actors involved. Therefore, existing research has proposed to anonymize social networks before outsourcing. A naive approach is to simply anonymize the identity of the social actors before outsourcing. An attacker that has some knowledge about a target’s neighborhood, especially a one-hop neighborhood, can still re-identify the target with high confidence. This attack, termed 1-neighborhood attack.