Let @math be a simple connected graph and @math an ordered subset of vertices. The metric representation of a vertex @math with respect to @math is the @math -vector @math , where @math represents the length of a shortest @math path in @math . The set @math is called a resolving set for @math if @math implies @math for every @math . The smallest cardinality of a resolving set is the metric dimension of @math . In this article we propose, to the best of our knowledge, a new problem in Graph Theory that resembles to the aforementioned metric dimension problem. We call @math a @math -antiresolving set if @math is the largest positive integer such that for every vertex @math there exist other @math different vertices @math with @math , , @math and @math have the same metric representation with respect to @math . The @math -metric antidimension of @math is the minimum cardinality among all the @math -antiresolving sets for @math . In this article, we introduce a novel privacy measure, named @math -anonymity and based on the @math -metric antidimension problem, aimed at evaluating the resistance of social graphs to active attacks. We, therefore, propose a true-biased algorithm for computing the @math -metric antidimension of random graphs. The success rate of our algorithm, according to empirical results, is above @math and @math when looking for a @math -antiresolving basis and a @math -antiresolving set respectively. We also investigate theoretical properties of the @math -antiresolving sets and the @math -metric antidimension of graphs. In particular, we focus on paths, cycles, complete bipartite graphs and trees.
Interested readers could refer to @cite_11 @cite_10 @cite_14 for further reading on privacy-preserving publication of social graphs.
@cite_14 @cite_10 @cite_11
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Continuing success of research on social and computer networks requires open access to realistic measurement datasets. While these datasets can be shared, generally in the form of social or Internet graphs, doing so often risks exposing sensitive user data to the public. Unfortunately, current techniques to improve privacy on graphs only target specific attacks, and have been proven to be vulnerable against powerful de-anonymization attacks. Our work seeks a solution to share meaningful graph datasets while preserving privacy. We observe a clear tension between strength of privacy protection and maintaining structural similarity to the original graph. To navigate the tradeoff, we develop a differentially-private graph model we call Pygmalion. Given a graph G and a desired level of e-differential privacy guarantee, Pygmalion extracts a graph's detailed structure into degree correlation statistics, introduces noise into the resulting dataset, and generates a synthetic graph G'. G' maintains as much structural similarity to G as possible, while introducing enough differences to provide the desired privacy guarantee. We show that simply applying differential privacy to graphs results in the addition of significant noise that may disrupt graph structure, making it unsuitable for experimental study. Instead, we introduce a partitioning approach that provides identical privacy guarantees using much less noise. Applied to real graphs, this technique requires an order of magnitude less noise for the same privacy guarantees. Finally, we apply our graph model to Internet, web, and Facebook social graphs, and show that it produces synthetic graphs that closely match the originals in both graph structure metrics and behavior in application-level tests. Nowadays, partly driven by many Web 2.0 applications, more and more social network data has been made publicly available and analyzed in one way or another. Privacy preserving publishing of social network data becomes a more and more important concern. In this paper, we present a brief yet systematic review of the existing anonymization techniques for privacy preserving publishing of social network data. We identify the new challenges in privacy preserving publishing of social network data comparing to the extensively studied relational case, and examine the possible problem formulation in three important dimensions: privacy, background knowledge, and data utility. We survey the existing anonymization methods for privacy preservation in two categories: clustering-based approaches and graph modification approaches. Social graphs, representing the online friendships among users, are one of the most fundamental types of data for many social media applications, such as recommendation, virality prediction and marketing. However, this data may be unavailable due to the privacy concerns of users, or kept privately by social network operators, which makes such applications difficult. One of the possible solutions to discover user connections is to use shared content, especially images on online social networks, such as Flickr and Instagram. This paper investigates how non-user generated labels annotated on shared images can be used for connection discovery with different color-based and feature-based methods. The label distribution is computed to represent users, and followee follower relationships are recommended based on the distribution similarity. These methods are evaluated with over 200k images from Flickr and it is proven that with non-user generated labels, user connections can be discovered, regardless of the method used. Feature-based methods are also proven to be 95 better than color-based methods, and 65 better than tag-based methods. The prevailing paradigm in Internet privacy literature, treating privacy within a context merely of rights and violations, is inadequate for studying the Internet as a social realm. Following Goffman on self-presentation and Altman's theorizing of privacy as an optimization between competing pressures for disclosure and withdrawal, the author investigates the mechanisms used by a sample (n = 704) of college students, the vast majority users of Facebook and Myspace, to negotiate boundaries between public and private. Findings show little to no relationship between online privacy concerns and information disclosure on online social network sites. Students manage unwanted audience concerns by adjusting profile visibility and using nicknames but not by restricting the information within the profile. Mechanisms analogous to boundary regulation in physical space, such as walls, locks, and doors, are favored; little adaptation is made to the Internet's key features of persistence, searchability, and cross-indexa...