Structural Vulnerabilities And Link Privacy

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Structural vulnerabilities and Link Privacy in Social Networks
In social networks, a link represents a relationship between two nodes in the network. These links can represent email conversations, web surfing, co-purchases of two or more products (e.g. Amazon), friendships (e.g. Facebook), followers (e.g. Twitter), etc. Often times these relationships are sensitive and/or confidential in nature [ying-wu] and the users are operating under the assumption that their private relationships will not be disclosed.
In recent years the amount of data accumulated from social networks has become very large, and there is a lot of valuable information to gain from analyzing and applying data mining to social network data.
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Neighborhood Randomization Using Sub-Graph Perturbation
In order for people to mine valuable data from social network graphs they must first be given information about the network. Even without explicit information about the nodes, an attacker may use structural information about the nodes and graph itself (e.g. node degree) to identify who the individuals are that the nodes represent. Simple graph-wise randomization addresses this problem by deleting k randomly chosen edges and replacing them with k randomly chosen edges, however a problem arises since data-miners depend on these structural attributes to properly analyze the social network. Fard and Wang [fard-wang] propose a structure-aware algorithm for the randomization of social network edges as well as a formal definition of “link privacy“ with respect to a probabilistic threshold. Their motivation is to help conceal sensitive links by using randomization techniques, without disturbing the actual structure of the graph, which is achieved through local neighborhood perturbation. This is needed so that graphs can be analyzed without the link structure being left entirely vulnerable to attackers. The goal of their algorithm is to make it so that an adversary cannot know if a link in the original graph exists from having a link in the new graph.
Problem definition: "Given a
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