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... Serious concerns on privacy protection in social networks have been raised in recent years; however, research in this area is still in its infancy. The problem is challenging due to the diversity and complexity of graph data, on which an adversary can use many types of background knowledge to conduct an attack. One popular type of attacks as studied by pioneer work [2] is the use of embedding subgraphs. We follow this line of work and identify two realistic targets of attacks, namely, NodeInfo and LinkInfo. Our investigations show that k-isomorphism, or anonymization by forming k pairwise isomorphic subgraphs, is both sufficient and necessary for the protection. The problem is shown to be NP-hard. We devise a number of techniques to enhance the anonymization efficiency while retaining the data utility. A compound vertex ID mechanism is also introduced for privacy preservation over multiple data releases. The satisfactory performance on a number of real datasets, including HEP-Th, EUemail and LiveJournal, illustrates that the high symmetry of social networks is very helpful in mitigating the difficulty of the problem. The problem of privacy-preserving data mining has attracted considerable attention in recent years because of increasing concerns about the privacy of the underlying data. In recent years, an important data domain which has emerged is that of graphs and structured data. Many data sets such as XML data, transportation networks, traffic in IP networks, social networks and hierarchically structured data are naturally represented as graphs. Existing work on graph privacy has focussed on the problem of anonymizing nodes or edges of a single graph, in which the identity is assumed to be associated with individual nodes. In this paper, we examine the more complex case, where we have a collection of graphs, and the identity is associated with individual graphs rather than nodes or edges. In such cases, the problem of identity anonymization is extremely difficult, since we need to not only anonymize the labels on the nodes, but also the underlying global structural information. In such cases, both the global and local structural information can be a challenge to the anonymization process, since any combination of such information can be used in order to de-identify the underlying graphs. In order to achieve this goal, we will create synthesized representations of the underlying graphs based on aggregate structural analytics of the collection of graphs. The synthesized graphs retain the properties of the original data while satisfying the k-anonymity requirement. Our experimental results show that the synthesized graphs maintain a high level of structural information and compatible classification accuracies with the original data. In this paper, we focus on the problem of preserving the privacy of sensitive relationships in graph data. We refer to the problem of inferring sensitive relationships from anonymized graph data as link reidentification. We propose five different privacy preservation strategies, which vary in terms of the amount of data removed (and hence their utility) and the amount of privacy preserved. We assume the adversary has an accurate predictive model for links, and we show experimentally the success of different link re-identification strategies under varying structural characteristics of the data. This paper intends to provide some insights of a scientific problem: how likely one's interests can be inferred from his her social connections -- friends, friends' friends, 3-degree friends, etc? Is "Birds of a Feather Flocks Together" a norm? We do not consider the friending activity on online social networking sites. Instead, we conduct this study by implementing a privacy-preserving large distribute social sensor system in a large global IT company to capture the multifaceted activities of 30,000+ people, including communications (e.g., emails, instant messaging, etc) and Web 2.0 activities (e.g., social bookmarking, file sharing, blogging, etc). These activities occupy the majority of employees' time in work, and thus, provide a high quality approximation to the real social connections of employees in the workplace context. In addition to such "informal networks", we investigated the "formal networks", such as their hierarchical structure, as well as the demographic profile data such as geography, job role, self-specified interests, etc. Because user ID matching across multiple sources on the Internet is very difficult, and most user activity logs have to be anonymized before they are processed, no prior studies could collect comparable multifaceted activity data of individuals. That makes this study unique. In this paper, we present a technique to predict the inference quality by utilizing (1) network analysis and network autocorrelation modeling of informal and formal networks, and (2) regression models to predict user interest inference quality from network characteristics. We verify our findings with experiments on both implicit user interests indicated by the content of communications or Web 2.0 activities, and explicit user interests specified in user profiles. We demonstrate that the inference quality prediction increases the inference quality of implicit interests by 42.8 , and inference quality of explicit interests by up to 101 . With the increasing prevalence of information networks, research on privacy-preserving network data publishing has received substantial attention recently. There are two streams of relevant research, targeting different privacy requirements. A large body of existing works focus on preventing node re-identification against adversaries with structural background knowledge, while some other studies aim to thwart edge disclosure. In general, the line of research on preventing edge disclosure is less fruitful, largely due to lack of a formal privacy model. The recent emergence of differential privacy has shown great promise for rigorous prevention of edge disclosure. Yet recent research indicates that differential privacy is vulnerable to data correlation, which hinders its application to network data that may be inherently correlated. In this paper, we show that differential privacy could be tuned to provide provable privacy guarantees even in the correlated setting by introducing an extra parameter, which measures the extent of correlation. We subsequently provide a holistic solution for non-interactive network data publication. First, we generate a private vertex labeling for a given network dataset to make the corresponding adjacency matrix form dense clusters. Next, we adaptively identify dense regions of the adjacency matrix by a data-dependent partitioning process. Finally, we reconstruct a noisy adjacency matrix by a novel use of the exponential mechanism. To our best knowledge, this is the first work providing a practical solution for publishing real-life network data via differential privacy. Extensive experiments demonstrate that our approach performs well on different types of real-life network datasets. Anonymized social network graphs published for academic or advertisement purposes are subject to de-anonymization attacks by leveraging side information in the form of a second, public social network graph correlated with the anonymized graph. This is because the two are from the same underlying graph of true social relationships. In this paper, we (i) characterize the maximum a posteriori (MAP) estimates of user identities for the anonymized graph and (ii) provide sufficient conditions for successful de-anonymization for underlying graphs with community structure. Our results generalize prior work that assumed underlying graphs of Erd o s-R 'enyi type, in addition to proving the optimality of the attack strategy adopted in the prior work. In this paper, we describe a comprehensive analysis of graph-theoretical properties of online social networks based on the Friend-of-a-Friend (FOAF) ontology. Of particular interest for this work were properties related to the small-world phenomenon. More than 1.6 million of the FOAF documents collected on the Semantic Web met our requirements and were analyzed in depth. Most FOAF documents are created and published by social networking services, blog hosting services, or combinations of the two as a matter of routine; only a fractional amount are maintained by individuals. Although the FOAF ontology defines unique identifiers for persons in theory, retrieval and particularly fusion of personal information is difficult and error-prone in practice. Nevertheless, we identified the largest strongly connected components of various community networks based on FOAF documents and analyzed them in regard to the small-world phenomenon. Interestingly, all components examined exhibited a characteristic path length comparable to the smallest length achievable for a graph of the respective size, and the clustering coefficient was much greater than expected for an equivalent random graph; along with power law degree distributions, both are typical features of small-world graphs. A large amount of valuable information resides in decentralized social graphs, where no entity has access to the complete graph structure. Instead, each user maintains locally a limited view of the graph. For example, in a phone network, each user keeps a contact list locally in her phone, and does not have access to other users' contacts. The contact lists of all users form an implicit social graph that could be very useful to study the interaction patterns among different populations. However, due to privacy concerns, one could not simply collect the unfettered local views from users and reconstruct a decentralized social network. In this paper, we investigate techniques to ensure local differential privacy of individuals while collecting structural information and generating representative synthetic social graphs. We show that existing local differential privacy and synthetic graph generation techniques are insufficient for preserving important graph properties, due to excessive noise injection, inability to retain important graph structure, or both. Motivated by this, we propose LDPGen, a novel multi-phase technique that incrementally clusters users based on their connections to different partitions of the whole population. Every time a user reports information, LDPGen carefully injects noise to ensure local differential privacy.We derive optimal parameters in this process to cluster structurally-similar users together. Once a good clustering of users is obtained, LDPGen adapts existing social graph generation models to construct a synthetic social graph. We conduct comprehensive experiments over four real datasets to evaluate the quality of the obtained synthetic graphs, using a variety of metrics, including (i) important graph structural measures; (ii) quality of community discovery; and (iii) applicability in social recommendation. Our experiments show that the proposed technique produces high-quality synthetic graphs that well represent the original decentralized social graphs, and significantly outperform those from baseline approaches. The concern of privacy has become an important issue for online social networks. In services such as Foursquare.com, whether a person likes an article is considered private and therefore not disclosed; only the aggregative statistics of articles (i.e., how many people like this article) is revealed. This paper tries to answer a question: can we predict the opinion holder in a heterogeneous social network without any labeled data? This question can be generalized to a link prediction with aggregative statistics problem. This paper devises a novel unsupervised framework to solve this problem, including two main components: (1) a three-layer factor graph model and three types of potential functions; (2) a ranked-margin learning and inference algorithm. Finally, we evaluate our method on four diverse prediction scenarios using four datasets: preference (Foursquare), repost (Twitter), response (Plurk), and citation (DBLP). We further exploit nine unsupervised models to solve this problem as baselines. Our approach not only wins out in all scenarios, but on the average achieves 9.90 AUC and 12.59 NDCG improvement over the best competitors. The resources are available at http: www.csie.ntu.edu.tw d97944007 aggregative Building on the popularity of online social networks (OSNs) such as Facebook, social content-sharing applications allow users to form communities around shared interests. Millions of users worldwide use them to share recommendations on everything from music and books to resources on the web. However, their increasing popularity is beginning to attract the attention of malicious attackers. As social network credentials become valued targets of phishing attacks and social worms, attackers look to leverage compromised accounts for further financial gain. In this paper, we analyze the state of privacy protection in social content-sharing applications, describe effective privacy attacks against today's social networks, and propose anonymization techniques to protect users. We show that simple protection mechanisms such as anonymizing shared data can still leave users open to social intersection attacks, where a small number of compromised users can identify the originators of shared content. Modeling this as a graph anonymization problem, we propose to provide users with k-anonymity privacy guarantees by augmenting the social graph with "latent edges." We identify StarClique, a locally minimal graph structure required for users to attain k-anonymity, where at worst, a user is identified as one of k possible contributors of a data object. We prove the correctness of our approach using analysis. Finally, using experiments driven by traces from the del.icio.us social bookmark site, we demonstrate the practicality and effectiveness of our approach on real-world systems. Recently, more and more social network data have been published in one way or another. Preserving privacy in publishing social network data becomes an important concern. With some local knowledge about individuals in a social network, an adversary may attack the privacy of some victims easily. Unfortunately, most of the previous studies on privacy preservation data publishing can deal with relational data only, and cannot be applied to social network data. In this paper, we take an initiative toward preserving privacy in social network data. Specifically, we identify an essential type of privacy attacks: neighborhood attacks. If an adversary has some knowledge about the neighbors of a target victim and the relationship among the neighbors, the victim may be re-identified from a social network even if the victim’s identity is preserved using the conventional anonymization techniques. To protect privacy against neighborhood attacks, we extend the conventional k-anonymity and l-diversity models from relational data to social network data. We show that the problems of computing optimal k-anonymous and l-diverse social networks are NP-hard. We develop practical solutions to the problems. The empirical study indicates that the anonymized social network data by our methods can still be used to answer aggregate network queries with high accuracy. Recently, as more and more social network data has been published in one way or another, preserving privacy in publishing social network data becomes an important concern. With some local knowledge about individuals in a social network, an adversary may attack the privacy of some victims easily. Unfortunately, most of the previous studies on privacy preservation can deal with relational data only, and cannot be applied to social network data. In this paper, we take an initiative towards preserving privacy in social network data. We identify an essential type of privacy attacks: neighborhood attacks. If an adversary has some knowledge about the neighbors of a target victim and the relationship among the neighbors, the victim may be re-identified from a social network even if the victim's identity is preserved using the conventional anonymization techniques. We show that the problem is challenging, and present a practical solution to battle neighborhood attacks. The empirical study indicates that anonymized social networks generated by our method can still be used to answer aggregate network queries with high accuracy. A key element of the social networks on the internet such as Facebook and Flickr is that they encourage users to create connections between themselves, other users and objects. One important task that has been approached in the literature that deals with such data is to use social graphs to predict user behavior (e.g. joining a group of interest). More specifically, we study the cold-start problem, where users only participate in some relations, which we will call social relations, but not in the relation on which the predictions are made, which we will refer to as target relations. We propose a formalization of the problem and a principled approach to it based on multi-relational factorization techniques. Furthermore, we derive a principled feature extraction scheme from the social data to extract predictors for a classifier on the target relation. Experiments conducted on real world datasets show that our approach outperforms current methods. The advent of the Internet has made the transmission of personally identifiable information more common and often unintended by the user. As personal information becomes more accessible, individuals worry that businesses misuse the information that is collected while they are online. Organizations have tried to mitigate this concern in two ways: (1) by offering privacy policies regarding the handling and use of personal information and (2) by offering benefits such as financial gains or convenience. In this paper, we interpret these actions in the context of the information-processing theory of motivation. Information-processing theories, also known as expectancy theories in the context of motivated behavior, are built on the premise that people process information about behavior-outcome relationships. By doing so, they are forming expectations and making decisions about what behavior to choose. Using an experimental setting, we empirically validate predictions that the means to mitigate privacy concerns are associated with positive valences resulting in an increase in motivational score. In a conjoint analysis exercise, 268 participants from the United States and Singapore face trade-off situations, where an organization may only offer incomplete privacy protection or some benefits. While privacy protections (against secondary use, improper access, and error) are associated with positive valences, we also find that financial gains and convenience can significantly increase individuals' motivational score of registering with a Web site. We find that benefits-monetary reward and future convenience-significantly affect individuals' preferences over Web sites with differing privacy policies. We also quantify the value of Web site privacy protection. Among U.S. subjects, protection against errors, improper access, and secondary use of personal information is worth @math 44.62. Finally, our approach also allows us to identify three distinct segments of Internet users-privacy guardians, information sellers, and convenience seekers. In recent years, concerns of privacy have become more prominent for social networks. Anonymizing a graph meaningfully is a challenging problem, as the original graph properties must be preserved as well as possible. We introduce a generalization of the degree anonymization problem posed by Liu and Terzi. In this problem, our goal is to anonymize a given subset of nodes while adding the fewest possible number of edges. The main contribution of this paper is an efficient algorithm for this problem by exploring its connection with the degree-constrained subgraph problem. Our experimental results show that our algorithm performs very well on many instances of social network data. Connections in distributed systems, such as social networks, online communities or peer-to-peer networks, form complex graphs. These graphs are of interest to scientists in fields as varied as marketing, epidemiology and psychology. However, knowledge of the graph is typically distributed among a large number of subjects, each of whom knows only a small piece of the graph. Efforts to assemble these pieces often fail because of privacy concerns: subjects refuse to share their local knowledge of the graph. To assuage these privacy concerns, we propose reconstructing the whole graph privately, i.e., in a way that hides the correspondence between the nodes and edges in the graph and the real-life entities and relationships that they represent. We first model the privacy threats posed by the private reconstruction of a distributed graph. Our model takes into account the possibility that malicious nodes may report incorrect information about the graph in order to facilitate later attempts to de-anonymize the reconstructed graph. We then propose protocols to privately assemble the pieces of a graph in ways that mitigate these threats. These protocols severely restrict the ability of adversaries to compromise the privacy of honest subjects.