Security of Online Social Networks

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1 Security of Online Social Networks Social Network Analysis Lehrstuhl IT-Sicherheitsmanagment Universität Siegen May 31, 2012 Lehrstuhl IT-Sicherheitsmanagment 1/25

2 Overview Lesson 06 Fundamental Graphs Motivation Graph Attributes Example Lehrstuhl IT-Sicherheitsmanagment 2/25

3 Motivation Analysis of structure Tell me who you know... Sociology, Mathematics, Computer Science important for Economics, Communication Theory, Psychology... Structures may decide fate of societies Georg Simmel (e.g. 1908) Lehrstuhl IT-Sicherheitsmanagment 3/25

4 Principle of Homophily similarity begets friendship (Plato 1968, p. 837) [2] divides society status vs value homophily indicators: Ethnicity, Gender, Age Religion (Protestant < Katholic < Jew) Education, Occupation, Social Class Behavior, Attitudes sources: Geography Family Ties Organisational Foci... Lehrstuhl IT-Sicherheitsmanagment 4/25

5 Applications Recommender Systems Social Recommender Targeted Advertising Friend Recommender solution classes person-oriented content-oriented location-oriented Lehrstuhl IT-Sicherheitsmanagment 5/25

6 Examples Friend Recommender Graph Improvement Lehrstuhl IT-Sicherheitsmanagment 6/25

7 Graph Attributes Lehrstuhl IT-Sicherheitsmanagment 7/25

8 A Social Network is a Graph... G = (V, E, p, a) V : vertices E : edges p : V personal attribs a : E link attribs Gross, Yellen: Graph Theory and its Applications, mostly Chapter 10 [3] Lehrstuhl IT-Sicherheitsmanagment 8/25

9 Graph Example g i h a d e b c f Lehrstuhl IT-Sicherheitsmanagment 9/25

10 Basic Vertex Attributes Distance Eccentricity Central Vertex Peripheral Vertex Total Distance Median Vertex Length of shortest path ecc(v) = max{d(v, w)} w V v : ecc(v) = min w V {ecc(w)} v : ecc(v) = max {ecc(w)} w V td(v) = d(v, w) w V v : td(v) = min w V {td(w)} Lehrstuhl IT-Sicherheitsmanagment 10/25

11 Vertex Centrality Describe Importance of Vertice Degree Number of Edges deg(v) Degree Centrality maximum Degree Betweenness Centrality Ratio of shortest paths bet(v) = s v t σ s,t(v) σ s,t Closeness Centrality aka Median Vertex Lehrstuhl IT-Sicherheitsmanagment 11/25

12 Basic Graph Attributes Connectedness a walk exists between any nodes Diameter Maximum of excentricities in G Radius Minimum of excentricities in G Center of a Graph Graph of central vertices Periphery of a Graph Graph of peripheral vertices Lehrstuhl IT-Sicherheitsmanagment 12/25

13 Domination Neighbours Dominating Set N(v) aka friends D V : v V : v D or v N(D) Distance-k Domination D V : v V : v D or w D : d(v, w) k Private Neighbour w is priv. neigh of v D iff N[w] D = {v} Independent Set S V : (no neighbours in S) Independent Dominating Set Lehrstuhl IT-Sicherheitsmanagment 13/25

14 Clique Complete Subgraph S G every v, w S no S : G S S circle of friends Lehrstuhl IT-Sicherheitsmanagment 14/25

15 3-Clique Example g i h a d e b c f Lehrstuhl IT-Sicherheitsmanagment 15/25

16 3-Clique Example g i h a d e b c f Lehrstuhl IT-Sicherheitsmanagment 16/25

17 Interpretation Centrality Importance of v Domination: efficient, wide influence Neighbours: similarity recommender Lehrstuhl IT-Sicherheitsmanagment 17/25

18 Graph Modells Erdős-Rényi Ramdom Graph G(n, m): n vertices, m edges uniform random from all G(n, m) ( probability ( n ) 1 2) m Scale-Free Networks (Barabasi) Degree follows power-law p(k) c k 1 [ Lehrstuhl IT-Sicherheitsmanagment 18/25

19 Example Dataset umbc-foafpub-2005-feb by Li Ding (ebiquity research group, CSEE, UMBC) Layout: gephi [4] Lehrstuhl IT-Sicherheitsmanagment 19/25

20 Example Lehrstuhl IT-Sicherheitsmanagment 20/25

21 Example Detail Lehrstuhl IT-Sicherheitsmanagment 21/25

22 Example Degrees at least power-law Lehrstuhl IT-Sicherheitsmanagment 22/25

23 Literatur I B. Wellmann and S. D. Berkowitz, Eds., Social Structures: A Network Approach. Cambridge: Cambridge University Press, M. McPherson, L. Smith-Lovin, and J. M. Cook, Birds of a feather: Homophily in social networks, Annual Review of Sociology, vol. 27, pp , [Online]. Available: J. L. Gross and J. Yellen, Graph Theory and its Applications, 2nd ed., ser. Discrete Mathematics and its Applications. Chapman & Hall/CRC, Lehrstuhl IT-Sicherheitsmanagment 23/25

24 Literatur II M. Bastian, S. Heymann, and M. Jacomy, Gephi: An open source software for exploring and manipulating networks, in Proceedings of International AAAI Conference on Weblogs and Social Media, [Online]. Available: http: // A. Narayanan and V. Shmatikov, De-anonymizing social networks, in Proceedings of the 30th IEEE Symposium on Security and Privacy (S&P 2009), May, Oakland, California, USA. IEEE Computer Society, 2009, pp [Online]. Available: shmat/shmat oak09.pdf Lehrstuhl IT-Sicherheitsmanagment 24/25

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