Conference Paper

Edge Anonymity in Social Network Graphs

Dept. of Comput. Sci., Univ. of Texas at San Antonio, San Antonio, TX, USA
Conference: Computational Science and Engineering, 2009. CSE '09. International Conference on, Volume: 4
Source: IEEE Xplore

ABSTRACT Edges in social network graphs may represent sensitive relationships. In this paper, we consider the problem of edges anonymity in graphs. We propose a probabilistic notion of edge anonymity, called graph confidence, which is general enough to capture the privacy breach made by an adversary who can pinpoint target persons in a graph partition based on any given set of topological features of vertexes. We consider a special type of edge anonymity problem which uses vertex degree to partition a graph. We analyze edge disclosure in real-world social networks and show that although some graphs can preserve vertex anonymity, they may still not preserve edge anonymity. We present three heuristic algorithms that protect edge anonymity using edge swap or edge deletion. Our experimental results, based on three real-world social networks and several utility measures, show that these algorithms can effectively preserve edge anonymity yet obtain anonymous graphs of acceptable utility.

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    • "k-isomorphism [9] is a way to achieve such structural similarity where the original graph is transformed into k disconnected pairwise isomorphic subgraphs through link insertion and deletion. Another approach is partitioning by nodes into equivalence classes and inducing edge equivalence classes grouping links between node classes[20]. In general, considerable structural distortion is required to provide the desired structural simi- larity. "
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    ABSTRACT: Link disclosure between two individuals in a social network could be a privacy breach. To limit link disclosure, previous works modeled a social network as an undirected graph and randomized a link over the entire domain of links, which leads to considerable structural distortion to the graph. In this work, we address this issue in two steps. First, we model a social network as a directed graph and randomize the destination of a link while keeping the source of a link intact. The randomization ensures that, if the prior belief about the destination of a link is bounded by some threshold, the posterior belief, given the published graph, is no more than another threshold. Then, we further reduce structural distortion by a subgraph-wise perturbation in which the given graph is partitioned into several subgraphs and randomization of destination nodes is performed within each subgraph. The benefit of subgraph-wise perturbation is that it retains a destination node with a higher retention probability and replaces a destination node with a node from a local neighborhood. We study the trade-off of utility and privacy of subgraph-wise perturbation.
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    • "Ying and Wu [16] investigate edge re-identification without considering the background knowledge of an adversary and perform random edge addition, edge deletion and edge swap for anonymization. Zhang et al. [17] assume that an adversary knows some vertex descriptions such as degrees , and propose reducing the probability of the existence of an edge linking two individuals by edge swap and edge deletion. The approach does not consider the resistance to vertex re-identification. "
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    ABSTRACT: Due to the rich information in graph data, the technique for privacy protection in published social networks is still in its infancy, as compared to the protection in relational databases. In this paper we identify a new type of attack called a friendship attack. In a friendship attack, an adversary utilizes the degrees of two vertices connected by an edge to re-identify related victims in a published social network data set. To protect against such attacks, we introduce the concept of k2-degree anonymity, which limits the probability of a vertex being re-identified to 1/k. For the k2-degree anonymization problem, we propose an Integer Programming formulation to find optimal solutions in small-scale networks. We also present an efficient heuristic approach for anonymizing large-scale social networks against friendship attacks. The experimental results demonstrate that the proposed approaches can preserve much of the characteristics of social networks.
    Proceedings of the 17th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, San Diego, CA, USA, August 21-24, 2011; 01/2011
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    • "Hay et al. [18] measure utility as degree distribution, diameter, path length, closeness centrality and betweenness centrality as well as clustering coefficient. Zhang [28] measures perturbation and utility by counting the number of modified edges and by degree distribution and clustering coefficients. "
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    ABSTRACT: You are on Facebook or you are out. Of course, this assessment is controversial and its rationale arguable. It is nevertheless not far, for many of us, from the reason behind our joining social media and publishing and sharing details of our professional and private lives. Not only the personal details we may reveal but also the very structure of the networks themselves are sources of invaluable information for any organization wanting to understand and learn about social groups, their dynamics and their members. These organizations may or may not be benevolent. It is therefore important to devise, design and evaluate solutions that guarantee some privacy. One approach that attempts to reconcile the different stakeholders' requirement is the publication of a modified graph. The perturbation is hoped to be sufficient to protect members' privacy while it maintains sufficient utility for analysts wanting to study the social media as a whole. It is necessarily a compromise. In this paper we try and empirically quantify the inevitable trade-off between utility and privacy. We do so for one state-of-the-art graph anonymization algorithm that protects against most structural attacks, the k-automorphism algorithm. We measure several metrics for a series of real graphs from various social media before and after their anonymization under various settings.
    iiWAS'2011 - The 13th International Conference on Information Integration and Web-based Applications and Services, 5-7 December 2011, Ho Chi Minh City, Vietnam; 01/2011
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