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Hiding in Social Networks University of Warsaw Faculty of Mathematics, Informatics and Mechanics Marcin Waniek Hiding in Social Networks PhD dissertation Supervisor dr hab. Piotr Faliszewski Department of Computer Science AGH University of Science and Technology Auxiliary Supervisor dr Tomasz Michalak Institute of Informatics University of Warsaw March 2017 Author’s declaration: I hereby declare that this dissertation is my own work. March 15, 2017 . Marcin Waniek Supervisor’s declaration: The dissertation is ready to be reviewed. March 15, 2017 . dr hab. Piotr Faliszewski Auxiliary Supervisor’s declaration: The dissertation is ready to be reviewed. March 15, 2017 . dr Tomasz Michalak Abstract The Internet and social media have fuelled enormous interest in social network analysis. New tools continue to be developed and used to analyse our personal connections. This raises privacy concerns that are likely to exacerbate in the future. With this in mind, we ask the question: Can individuals or groups actively manage their connections to evade social network analysis tools? By addressing this question, the general public may better protect their privacy, oppressed activist groups may better conceal their existence, and security agencies may better understand how terrorists escape detection. In this dissertation we consider hiding from three different types of social network analysis tools. First, we study how both an individual and a group of nodes can evade analysis utilizing centrality measures, without compromising ability to participate in net- work’s activities. In the second study, we investigate how a community can avoid being identified by a community detection algorithm as a closely cooperating group of nodes. In the third study, we analyse how a presence of a particular edge in a network can be hidden from link prediction algorithms. For considered problems we analyse their computational complexity and prove that they are usually NP-hard. However, we also provide polynomial-time heuristic solutions that turn out to be effective in practice. We test our algorithms on a number of real-life and artificially generated network datasets. Keywords: Social networks; Hiding in networks; Centrality measures; Influence mod- els; Community detection; Link prediction; Computational complexity; Heuristic solu- tions. ACM classification: Security and privacy → Social network security and privacy. Theory of computation → Social networks. Theory of computation → Problems, reductions and completeness. Streszczenie Internet oraz media społecznościowe spowodowały ogromny wzrost zainteresowania meto- dami analizy sieci społecznych. Coraz bardziej zaawansowane narzędzia służą do analizy naszych powiązań z innymi ludźmi. Rodzi to poważne obawy związane z prywatnością. Mając to na uwadze, rozważamy następujące pytanie: Czy członek lub grupa członków sieci społecznej może aktywnie zarządzać swoimi połączeniami tak, aby uniknąć wykrycia przez narzędzia analizy sieci społecznych? Odpowiedź na to pytanie pozwoliłaby użyt- kownikom Internetu lepiej chronić swoją prywatność, grupom aktywistów lepiej ukrywać swoją działalność, a agencjom bezpieczeństwa lepiej rozumieć w jaki sposób organizacje terrorystyczne i kryminalne mogą unikać wykrycia. W tej pracy rozważamy ukrywanie się przed trzema różnymi narzędziami analizy sieci społecznych. Po pierwsze, badamy jak pojedynczy węzeł lub ich grupa może uniknąć wy- krycia przez miary centralności (ang. centrality measures), wciąż pozostając zdolnym do brania udziału w działalności sieci. Po drugie, analizujemy jak grupa węzłów może uniknąć zidentyfikowania przez algorytmy wykrywania społeczności (ang. community detection al- gorithms). Po trzecie wreszcie, badamy jak można ukryć istnienie określonej krawędzi w sieci przed algorytmami przewidywania połączeń (ang. link prediction algorithms). Analizujemy złożoność obliczeniową rozważanych zagadnień oraz udowadniamy, że większość z nich to problemy NP-trudne. Tym niemniej prezentujemy również wielomia- nowe rozwiązania heurystyczne, które okazują się efektywne w praktyce. Nasze algorytmy testujemy na szeregu różnych sieci, tak prawdziwych, jak i wygenerowanych losowo. Słowa kluczowe: Sieci społeczne; Ukrywanie się w sieciach; Miary centralności; Modele wpływu; Wykrywanie społeczności; Przewidywanie połączeń; Złożoność oblicze- niowa; Rozwiązania heurystyczne. Klasyfikacja ACM: Bezpieczeństwo i prywatność → Bezpieczeństwo i pry- watność w sieciach społecznych. Teoria obliczeń → Sieci społeczne. Teoria ob- liczeń → Preoblemy, redukcje i zupełność. Acknowledgments I would like to express my deepest gratitude to Tomasz Michalak, my mentor and supervisor, who taught me almost all I know about research (with the rest coming from other people mentioned on this page). I would not be where I am today without him. I am thankful to Piotr Faliszewski, who helped me put together this dissertation and greatly improved the quality of my writing. I am grateful to Talal Rahwan, discussions with whom influenced many parts of this dissertation and whose hospitality made far away country feel like home. I would also like to thank all my other co-authors in this and other lines of research: Michael Wooldridge, Long Tran-Thanh, Agata Nieścieruk, Nicholas Jennings, Marcin Bielecki, Joanna Tyrowicz and Krzysztof Makarski. I have learned a lot from all of them. Finally, I would like to give thanks to my family and my friends, especially to my mom, my dad, and my brother Paweł. Finishing this dissertation would not be possible without their constant love and support. My work was supported by the Polish National Science Centre grant Hiding in Social Networks, no. 2015/17/N/ST6/03686. Contents 1 Introduction 4 1.1 Motivation . .4 1.2 Organization and Results . .6 1.3 Related Work . .7 1.3.1 Link Recommendation . .7 1.3.2 Sensitivity Analysis . .8 1.3.3 Dark Networks Analysis . .9 1.4 Publications . 11 2 Preliminaries 13 2.1 Basic Network Notation . 13 2.2 Datasets . 14 2.3 Computational Complexity . 16 2.3.1 The Turing Machine . 16 2.3.2 Complexity Classes and Reduction Process . 17 2.3.3 NP-Complete Problems . 18 3 Disguising Centrality of a Node 19 3.1 Introduction . 19 3.2 Preliminaries . 20 3.2.1 Centrality Measures . 21 3.2.2 Models of Influence . 21 3.3 Problem Definitions . 23 3.4 Complexity Analysis . 24 3.5 Heuristic Solution . 33 3.5.1 The ROAM heuristic . 33 3.5.2 Configuring the ROAM Heuristic . 35 3.5.3 Experimental Results . 35 3.6 Concluding Remarks . 38 4 Hiding Leaders 41 4.1 Introduction . 41 4.2 Problem Definition . 43 4.3 Complexity Analysis . 44 4.4 Constructing a Network . 54 4.5 Concluding Remarks . 58 2 5 Hiding Communities 61 5.1 Introduction . 61 5.2 Preliminaries . 62 5.3 Minimizing Modularity . 63 5.4 Measure of Concealment . 67 5.5 Heuristic Solution . 68 5.5.1 The DICE Heuristic . 68 5.5.2 Experimental Results . 69 5.6 Concluding Remarks . 71 6 Evading Link Prediction 74 6.1 Introduction . 74 6.2 Preliminaries . 75 6.3 Problem Definition . 77 6.4 Complexity Analysis . 78 6.5 Heuristic Solution . 83 6.5.1 The Effects of Adding or Removing an Edge . 84 6.5.2 The OTC Heuristic . 85 6.5.3 The CTR Heuristic . 86 6.5.4 Experimental Design . 87 6.5.5 Simulation Results . 88 6.6 Concluding Remarks . 91 7 Conclusions 93 Bibliography 97 A ROAM Simulation Results 109 B DICE Simulation Results 121 C Remainder of the Proof of Lemma 1 126 D An Efficient Implementation of the OTC algorithm 132 E Priority Queue Implementation of the CTR algorithm 134 F OTC and CTR Simulation Results 135 3 Chapter 1 Introduction In this chapter we introduce the issue of hiding in social networks and we outline the organization of this dissertation. Next, we present the body of related literature. Finally, we list our publications that contain elements of this dissertation. 1.1 Motivation Recent years have lead to an increased interest in the analysis of social networks [131]. Applications of this wide body of research vary from organizing massive viral-marketing campaigns [31], through the analysis of outbreaks of infectious diseases [56], all the way up to fighting global criminal and terrorist organizations [98, 141]. Such a variety of problems gave rise to various social network analysis tools and techniques. Examples of prominent types of tools include centrality measures, community detection algorithms, and link prediction algorithms. Centrality measures [12] are tools to identify key nodes in the network, being it the leader of a terrorist cell [80], the financial institution responsible for the financial crisis [82] or the most important airport in the world-wide air transportation structure [60]. Community detection algorithms [51] can extract communities of closely cooperating individuals from the network data, e.g., associates of a known criminal [49], climate indices related to seasonal rainfall [14] or protein complexes in the interaction diagram [112]. Link prediction algorithms [57] can asses probabilities of existence of hidden or not-yet-formed edges, either to detect missing connections between mafia members [15], to discover the interactions between proteins in biological networks [26], or to recommend to customer a product that she might be interested in buying [37, 88]. Clearly, many situations, where social network analysis tools are being applied can be described as adversarial settings. In other words, members of the networks that are being analysed may be interested in falsifying the results of such analysis, e.g., by modifying the structure of their social connections. At the same time, however, nearly all
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