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In this paper we introduce a general version of the anonymization problem in social networks, in which the goal is to maximize the number of anonymous nodes by altering a given graph. We define three variants of this optimization problem, being full, partial and budgeted anonymization. In each, the objective is to maximize the number of k-anonymous nodes, i.e., nodes for which there are at least k-1 equivalent nodes, according to a particular anonymity measure of structural node equivalence. We propose six new heuristic algorithms for solving the anonymization problem which we implement into the reusable ANO-NET computational framework. As a baseline, we use an edge sampling method introduced in previous work. Experiments on both graph models and 17 real-world network datasets result in three empirical findings. First, we demonstrate that edge deletion is the most effective graph alteration operation. Second, we compare four commonly used anonymity measures from the literature and highlight how the choice of anonymity measure has a tremendous effect on both the achieved anonymity as well as the difficulty of solving the anonymization problem. Third, we find that the proposed algorithms that preferentially delete edges with a larger effect on nodes at a structurally unique position consistently outperform heuristics solely based on network structure. With similar runtimes, our algorithms retain on average 17 times more edges, ensuring higher data utility after full anonymization. In the budgeted variant, they achieve 4.4 times more anonymous nodes than the baseline. This work lays important foundations for future development of algorithms for anonymizing social networks.

Privacy-aware sharing of network data is a difficult task due to the interconnectedness of individuals in networks. An important part of this problem is the inherently difficult question of how in a particular situation the privacy of an individual node should be measured. To that end, in this paper we propose a set of aspects that one should consider when choosing a measure for privacy. These aspects include the type of desired privacy and attacker scenario against which the measure protects, utility of the data, the type of desired output, and the computational complexity of the chosen measure. Based on these aspects, we provide a systematic overview of existing approaches in the literature. We then focus on a set of measures that ultimately enables our objective: sharing the anonymized full network dataset with limited disclosure risk. The considered measures, each based on the concept of k-anonymity, account for the structure of the surroundings of a certain node and differ in completeness and reach of the structural information taken into account. We present a comprehensive theoretical characterization as well as comparative empirical experiments on a wide range of real-world network datasets with up to millions of edges. We find that the choice of the measure has an enormous effect on aforementioned aspects. Most interestingly, we find that the most effective measures consider a greater node vicinity, yet utilize minimal structural information and thus use minimal computational resources. This finding has important implications for researchers and practitioners, who may, based on the recommendations given in this paper, make an informed choice on how to safely share large-scale network data in a privacy-aware manner.

Dark Web Marketplaces (DWM) facilitate the online trade of illicit goods. Due to the illicit nature of these marketplaces, quality datasets are scarce and difficult to produce. The Dark Net Market archives (2015) presented raw scraped source files crawled from a selection of DWMs, including Evolution. Here, we present, specifically for the Evolution DWM, a structured dataset extracted from Dark Net Market archive data. Uniquely, many of the data quality issues inherent to crawled data are resolved. The dataset covers over 500 thousand forum posts and over 80 thousand listings, providing data on forums, topics, posts, forum users, market vendors, listings, and more. Additionally, we present temporal weighted communication networks extracted from this data. The presented dataset provides easy access to a high quality DWM dataset to facilitate the study of criminal behaviour and communication on such DWMs, which may provide a relevant source of knowledge for researchers across disciplines, from social science to law to network science., Comment: 19 pages, 5 figures

In this work we focus on identifying key players in dark net cryptomarkets that facilitate online trade of illegal goods. Law enforcement aims to disrupt criminal activity conducted through these markets by targeting key players vital to the market's existence and success. We particularly focus on detecting successful vendors responsible for the majority of illegal trade. Our methodology aims to uncover whether the task of key player identification should center around plainly measuring user and forum activity, or that it requires leveraging specific patterns of user communication. We focus on a large-scale dataset from the Evolution cryptomarket, which we model as an evolving communication network. Results indicate that user and forum activity, measured through topic engagement, is best able to identify successful vendors. Interestingly, considering users with higher betweenness centrality in the communication network further improves performance, also identifying successful vendors with moderate activity on the forum. But more importantly, analyzing the forum data over time, we find evidence that attaining a high betweenness score comes before vendor success. This suggests that the proposed network-driven approach of modelling user communication might prove useful as an early warning signal for key player identification., Comment: Text and analysis updated based on reviewer comments and Supplementary Material added

Ensuring privacy of individuals is of paramount importance to social network analysis research. Previous work assessed anonymity in a network based on the non-uniqueness of a node's ego network. In this work, we show that this approach does not adequately account for the strong de-anonymizing effect of distant connections. We first propose the use of d-k-anonymity, a novel measure that takes knowledge up to distance d of a considered node into account. Second, we introduce anonymity-cascade, which exploits the so-called infectiousness of uniqueness: mere information about being connected to another unique node can make a given node uniquely identifiable. These two approaches, together with relevant "twin node" processing steps in the underlying graph structure, offer practitioners flexible solutions, tunable in precision and computation time. This enables the assessment of anonymity in large-scale networks with up to millions of nodes and edges. Experiments on graph models and a wide range of real-world networks show drastic decreases in anonymity when connections at distance 2 are considered. Moreover, extending the knowledge beyond the ego network with just one extra link often already decreases overall anonymity by over 50%. These findings have important implications for privacy-aware sharing of sensitive network data., Comment: New version. Updated title, and results added to Supplementary information

Community detection is a well established method for studying the meso scale structure of social networks. Applying a community detection algorithm results in a division of a network into communities that is often used to inspect and reason about community membership of specific nodes. This micro level interpretation step of community structure is a crucial step in typical social science research. However, the methodological caveat in this step is that virtually all modern community detection methods are non-deterministic and based on randomization and approximated results. This needs to be explicitly taken into consideration when reasoning about community membership of individual nodes. To do so, we propose a metric of community membership consistency, that provides node-level insights in how reliable the placement of that node into a community really is. In addition, it enables us to distinguish the community core members of a community. The usefulness of the proposed metrics is demonstrated on corporate board interlock networks, in which weighted links represent shared senior level directors between firms. Results suggest that the community structure of global business groups is centered around persistent communities consisting of core countries tied by geographical and cultural proximity. In addition, we identify fringe countries that appear to associate with a number of different global business communities., Comment: This manuscript has been accepted for publication in the Journal of Computational Social Science

Nowadays, social networks of ever increasing size are studied by researchers from a range of disciplines. The data underlying these networks is often automatically gathered from API's, websites or existing databases. As a result, the quality of this data is typically not manually validated, and the resulting networks may be based on false, biased or incomplete data. In this paper, we investigate the effect of data quality issues on the analysis of large networks. We focus on the global board interlock network, in which nodes represent firms across the globe, and edges model social ties between firms -- shared board members holding a position at both firms. First, we demonstrate how we can automatically assess the completeness of a large dataset of 160 million firms, in which data is missing not at random. Second, we present a novel method to increase the accuracy of the entries in our data. By comparing the expected and empirical characteristics of the resulting network topology, we develop a technique that automatically prunes and merges duplicate nodes and edges. Third, we use a case study of the board interlock network of Sweden to show how poor quality data results in incorrect network topologies, biased centrality values and abnormal influence spread under a well-known diffusion model. Finally, we demonstrate how our data quality assessment methods help restore the correct network structure, ultimately allowing us to derive meaningful and correct results from analyzing the network.

Corporations across the world are highly interconnected in a large global network of corporate control. This paper investigates the global board interlock network, covering 400,000 firms linked through 1,700,000 edges representing shared directors between these firms. The main focus is on the concept of centrality, which is used to investigate the embeddedness of firms from a particular country within the global network. The study results in three contributions. First, to the best of our knowledge for the first time we can investigate the topology as well as the concept of centrality in corporate networks at a global scale, allowing for the largest cross-country comparison ever done in interlocking directorates literature. We demonstrate, amongst other things, extremely similar network topologies, yet large differences between countries when it comes to the relation between economic prominence indicators and firm centrality. Second, we introduce two new metrics that are specifically suitable for comparing the centrality ranking of a partition to that of the full network. Using the notion of centrality persistence we propose to measure the persistence of a partition's centrality ranking in the full network. In the board interlock network, it allows us to assess the extent to which the footprint of a national network is still present within the global network. Next, the measure of centrality ranking dominance tells us whether a partition (country) is more dominant at the top or the bottom of the centrality ranking of the full (global) network. Finally, comparing these two new measures of persistence and dominance between different countries allows us to classify these countries based the their embeddedness, measured using the relation between the centrality of a country's firms on the national and the global scale of the board interlock network., Comment: 27 pages

Business elites reconfigure their locus of organization over time, from the city level, to the national level, and beyond. We ask what the current level of elite organization is and propose a novel theoretical and empirical approach to answer this question. Building on the universal distinction between local and nonlocal ties we use network analysis and community detection to dissect the global network of interlocking directorates among over five million firms. We find that elite orientation is indeed changing from the national to the transnational plane, but we register a considerable heterogeneity across different regions in the world. In some regions the business communities are organized along national borders, whereas in other areas the locus of organization is at the city level or international level. London dominates the global corporate elite network. Our findings underscore that the study of corporate elites requires an approach that is sensitive to levels of organization that go beyond the confines of nation states., Comment: 29 pages