Networks are structures that describe a set of entities and the relations between them. A social network, for example, provides information on individuals in some population and the links between them, which may describe relations of friendship, collaboration, correspondence and so forth. An information network, as another example, may describe scientific publications and their citation links. The nodes of the graph correspond to the entities, while edges denote relations between them. Real social networks may be more complex or contain additional information. the graph would be directed; if the interaction involves more than two parties (e.g., a social network that describes co-membership in social clubs) then the network would be modeled as a hyper-graph; There are several types of interaction, the edges would be labeled; or the nodes in the graph could be accompanied by attributes that provide demographic information such as age, gender, location or occupation which could enrich and shed light on the structure of the network. the data in such social networks cannot be released as is, since it might contain sensitive information. A naive anonymization of the network, in the sense of removing identifying attributes like names or social security numbers from the data, is insufficient. The mere structure of the released graph may reveal the identity of the individuals behind some of the nodes. The methods of the first category provide k-anonymity via a deterministic procedure of edge additions or deletions. Those methods it is assumed that the adversary has a background knowledge regarding some property of its target node, and then those methods modify the graph so that it becomes k-anonymous with respect to that assumed property. The methods of the second category add noise to the data, in the form of random additions, deletions or switching of edges, in order to prevent adversaries from identifying their target in the network, or inferring the existence of links between nodes
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