The advent of social networks poses severe threats on user privacy as adversaries can de-anonymize users' identities by mapping them to correlated cross-domain networks. Without ground-truth mapping, prior literature proposes various cost functions in hope of measuring the quality of mappings. However, there is generally a lacking of rationale behind the cost functions, whose minimizer also remains algorithmically unknown. We jointly tackle above concerns under a more practical social network model parameterized by overlapping communities, which, neglected by prior art, can serve as side information for de-anonymization. Regarding the unavailability of ground-truth mapping to adversaries, by virtue of the Minimum Mean Square Error (MMSE), our first contribution is a well-justified cost function minimizing the expected number of mismatched users over all possible true mappings. While proving the NP-hardness of minimizing MMSE, we validly transform it into the weighted-edge matching problem (WEMP), which, as disclosed theoretically, resolves the tension between optimality and complexity: (i) WEMP asymptotically returns a negligible mapping error in large network size under mild conditions facilitated by higher overlapping strength; (ii) WEMP can be algorithmically characterized via the convex-concave based de-anonymization algorithm (CBDA), perfectly finding the optimum of WEMP. Extensive experiments further confirm the effectiveness of CBDA under overlapping communities, in terms of averagely 90 re-identified users in the rare true cross-domain co-author networks when communities overlap densely, and roughly 70 enhanced re-identification ratio compared to non-overlapping cases.
However, in real situations it is often the case that adversaries are difficult to obtain seeded nodes before de-anonymizing @cite_3 @cite_22 due to the limited access to user profiles. For seedless networks, the major methodology is to propose cost functions and obtain an estimation of the correct mapping between two networks by optimizing these cost functions. Pedarsani and Grossglauer @cite_5 are the precursors in de-anonymizing seedless networks. They studied this problem under Erdos-Renyi graph and their cost function was the number of mismatched edges. With the same cost function, @cite_13 considered the situation where the nodes in two networks are overlapping partially, and Cullina and Kiyavash @cite_26 further investigated the information-theoretic threshold for exact identification in @cite_5 . However, the cost functions in @cite_5 @cite_13 @cite_26 were not justified by rationale. One cost function based on Maximum A Posterior (MAP) has been justified by @cite_15 @cite_3 @cite_22 . @cite_15 theoretically proved the validity of MAP and @cite_3 @cite_22 provided two approximation algorithms to solve this problem.
@cite_26 @cite_22 @cite_3 @cite_5 @cite_15 @cite_13
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We consider the problem of perfectly recovering the vertex correspondence between two correlated Erdos-Renyi (ER) graphs. For a pair of correlated graphs on the same vertex set, the correspondence between the vertices can be obscured by randomly permuting the vertex labels of one of the graphs. In some cases, the structural information in the graphs allow this correspondence to be recovered. We investigate the information-theoretic threshold for exact recovery, i.e. the conditions under which the entire vertex correspondence can be correctly recovered given unbounded computational resources. Pedarsani and Grossglauser provided an achievability result of this type. Their result establishes the scaling dependence of the threshold on the number of vertices. We improve on their achievability bound. We also provide a converse bound, establishing conditions under which exact recovery is impossible. Together, these establish the scaling dependence of the threshold on the level of correlation between the two graphs. The converse and achievability bounds differ by a factor of two for sparse, significantly correlated graphs. A crucial privacy-driven issue nowadays is re-identifying anonymized social networks by mapping them to correlated cross-domain auxiliary networks. Prior works are typically based on modeling social networks as random graphs representing users and their relations, and subsequently quantify the quality of mappings through cost functions that are proposed without sufficient rationale. Also, it remains unknown how to algorithmically meet the demand of such quantifications, i.e., to find the minimizer of the cost functions. We address those concerns in a more realistic social network modeling parameterized by community structures that can be leveraged as side information for de-anonymization. By Maximum A Posteriori (MAP) estimation, our first contribution is new and well justified cost functions, which, when minimized, enjoy superiority to previous ones in finding the correct mapping with the highest probability. The feasibility of the cost functions is then for the first time algorithmically characterized. While proving the general multiplicative inapproximability, we are able to propose two algorithms, which, respectively, enjoy an -additive approximation and a conditional optimality in carrying out successful user re-identification. Our theoretical findings are empirically validated, with a notable dataset extracted from rare true cross-domain networks that reproduce genuine social network de-anonymization. Both theoretical and empirical observations also manifest the importance of community information in enhancing privacy inferencing. The proliferation of online social networks, and the concomitant accumulation of user data, give rise to hotly debated issues of privacy, security, and control. One specific challenge is the sharing or public release of anonymized data without accidentally leaking personally identifiable information (PII). Unfortunately, it is often difficult to ascertain that sophisticated statistical techniques, potentially employing additional external data sources, are unable to break anonymity. In this paper, we consider an instance of this problem, where the object of interest is the structure of a social network, i.e., a graph describing users and their links. Recent work demonstrates that anonymizing node identities may not be sufficient to keep the network private: the availability of node and link data from another domain, which is correlated with the anonymized network, has been used to re-identify the anonymized nodes. This paper is about conditions under which such a de-anonymization process is possible. We attempt to shed light on the following question: can we assume that a sufficiently sparse network is inherently anonymous, in the sense that even with unlimited computational power, de-anonymization is impossible? Our approach is to introduce a random graph model for a version of the de-anonymization problem, which is parameterized by the expected node degree and a similarity parameter that controls the correlation between two graphs over the same vertex set. We find simple conditions on these parameters delineating the boundary of privacy, and show that the mean node degree need only grow slightly faster than log n with network size n for nodes to be identifiable. Our results have policy implications for sharing of anonymized network information. 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. Network alignment refers to the problem of matching the vertex sets of two unlabeled graphs, which can be viewed as a generalization of the classic graph isomorphism problem. Network alignment has applications in several fields, including social network analysis, privacy, pattern recognition, computer vision, and computational biology. A number of heuristic algorithms have been proposed in these fields. Recent progress in the analysis of network alignment over stochastic models sheds light on the interplay between network parameters and matchability. In this paper, we consider the alignment problem when the two networks overlap only partially, i.e., there exist vertices in one network that have no counterpart in the other. We define a random bigraph model that generates two correlated graphs G1,2; it is parameterized by the expected node overlap t2 and by the expected edge overlap s2. We define a cost function for structural mismatch under a particular alignment, and we identify a threshold for perfect matchability: if the average node degrees of G1,2 grow as ω((s−2t−1 log(n)), then minimization of the proposed cost function results in an alignment which (i) is over exactly the set of shared nodes between G1 and G2, and (ii) agrees with the true matching between these shared nodes. Our result shows that network alignment is fundamentally robust to partial edge and node overlaps.