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Social Networks: Prestige, Centrality, and Influence

(Invited Paper)

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Relational and Algebraic Methods in Computer Science (RAMICS 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6663))

Abstract

We deliver a short overview of different centrality measures and influence concepts in social networks, and present the relation-algebraic approach to the concepts of power and influence. First, we briefly discuss four kinds of measures of centrality: the ones based on degree, closeness, betweenness, and the eigenvector-related measures. We consider centrality of a node and of a network. Moreover, we give a classification of the centrality measures based on a topology of network flows. Furthermore, we present a certain model of influence in a social network and discuss some applications of relation algebra and RelView to this model.

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References

  1. Ballester, C., Calvo-Armengol, A., Zenou, Y.: Who’s Who in Networks. Wanted: The Key Player. Econometrica 74, 1403–1417 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  2. Banzhaf, J.: Weighted Voting Doesn’t Work: A Mathematical Analysis. Rutgers Law Review 19, 317–343 (1965)

    Google Scholar 

  3. Behnke, R., Berghammer, R., Meyer, E., Schneider, P.: RelView - A system for calculating with relations and relational programming. In: Astesiano, E. (ed.) ETAPS 1998 and FASE 1998. LNCS, vol. 1382, pp. 318–321. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  4. Berghammer, R., Karger, B., von Ulke, C.: Relation-algebraic Analysis of Petri Nets with RelView. In: Margaria, T., Steffen, B. (eds.) TACAS 1996. LNCS, vol. 1055, pp. 49–69. Springer, Heidelberg (1996)

    Chapter  Google Scholar 

  5. Berghammer, R., Rusinowska, A., De Swart, H.: Applying Relational Algebra and RelView to Coalition Formation. EJOR 178/2, 530–542 (2007)

    Article  MATH  Google Scholar 

  6. Berghammer, R., Rusinowska, A., De Swart, H.: An Interdisciplinary Approach to Coalition Formation. EJOR 195, 487–496 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  7. Berghammer, R., Rusinowska, A., De Swart, H.: Applying Relational Algebra and RelView to Measures in a Social Network. EJOR 202, 182–195 (2010)

    Article  MATH  Google Scholar 

  8. Berghammer, R., Bolus, S., Rusinowska, A., De Swart, H.: A Relation-algebraic Approach to Simple Games. EJOR 210, 68–80 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  9. Berghammer, R., Schmidt, G., Winter, M.: RelView and Rath – Two Systems for Dealing with Relations. In: De Swart et al. (eds.) pp. 1–16 (2003)

    Google Scholar 

  10. Bonacich, P.: Factoring and Weighting Approaches to Status Scores and Clique Identification. Journal of Mathematical Sociology 2, 113–120 (1972)

    Article  Google Scholar 

  11. Bonacich, P.: Power and Centrality: A Family of Measures. American Journal of Sociology 92, 1170–1182 (1987)

    Article  Google Scholar 

  12. Borgatti, S.P.: Centrality and Network Flow. Social Networks 27, 55–71 (2005)

    Article  Google Scholar 

  13. Brink, C., Kahl, W., Schmidt, G. (eds.): Relational Methods in Computer Science. Advances in Computing Science. Springer, Heidelberg (1997)

    MATH  Google Scholar 

  14. DeGroot, M.H.: Reaching a Consensus. Journal of the American Statistical Association 69, 118–121 (1974)

    Article  MATH  Google Scholar 

  15. DeMarzo, P., Vayanos, D., Zwiebel, J.: Persuasion Bias, Social Influence, and Unidimensional Opinions. Quarterly Journal of Economics 118, 909–968 (2003)

    Article  MATH  Google Scholar 

  16. De Swart, H., Orłowska, E., Schmidt, G., Roubens, M. (eds.): Theory and Applications of Relational Structures as Knowledge Instruments. LNCS, vol. 2929. Springer, Heidelberg (2003)

    MATH  Google Scholar 

  17. De Swart, H., Orłowska, E., Schmidt, G., Roubens, M. (eds.): TARSKI 2006. LNCS (LNAI), vol. 4342. Springer, Heidelberg (2006)

    Google Scholar 

  18. Freeman, L.: A Set of Measures of Centrality Based on Betweenness. Sociometry 40, 35–41 (1977)

    Article  Google Scholar 

  19. Freeman, L.: Centrality in Social Networks: Conceptual Clarification. Social Networks 1, 215–239 (1979)

    Article  Google Scholar 

  20. Friedkin, N.E., Johnsen, E.C.: Social Influence and Opinions. Journal of Mathematical Sociology 15, 193–206 (1990)

    Article  MATH  Google Scholar 

  21. Friedkin, N.E., Johnsen, E.C.: Social Positions in Influence Networks. Social Networks 19, 209–222 (1997)

    Article  Google Scholar 

  22. Golub, B., Jackson, M.O.: Naïve Learning in Social Networks and the Wisdom of Crowds. American Economic Journal: Microeconomics 2(1), 112–149 (2010)

    Google Scholar 

  23. Goyal, S.: Connections: An Introduction to the Economics of Networks. Princeton University Press, Princeton (2007)

    MATH  Google Scholar 

  24. Grabisch, M., Rusinowska, A.: Measuring Influence in Command Games. Social Choice and Welfare 33, 177–209 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  25. Grabisch, M., Rusinowska, A.: A Model of Influence in a Social Network. Theory and Decision 69(1), 69–96 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  26. Grabisch, M., Rusinowska, A.: A Model of Influence with an Ordered Set of Possible Actions. Theory and Decision 69(4), 635–656 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  27. Grabisch, M., Rusinowska, A.: Different Approaches to Influence Based on Social Networks and Simple Games. In: Van Deemen, A., Rusinowska, A. (eds.) Collective Decision Making: Views from Social Choice and Game Theory. Series Theory and Decision Library C, vol. 43, pp. 185–209. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  28. Grabisch, M., Rusinowska, A.: A Model of Influence with a Continuum of Actions. GATE Working Paper, 2010-04 (2010)

    Google Scholar 

  29. Grabisch, M., Rusinowska, A.: Iterating Influence Between Players in a Social Network. CES Working Paper, 2010.89 (2010)

    Google Scholar 

  30. Grabisch, M., Rusinowska, A.: Influence Functions, Followers and Command Games. Games and Economic Behavior (forthcoming), doi: 10.1016/j.geb.2010.06.003

    Google Scholar 

  31. Grofman, B., Owen, G.: A Game Theoretic Approach to Measuring Degree of Centrality in Social Networks. Social Networks 4, 213–224 (1982)

    Article  MathSciNet  Google Scholar 

  32. Hendrickx, R., Borm, P., Van den Brink, R., Owen, G.: The VL Control Measure for Symmetric Networks. Social Networks 31, 85–91 (2009)

    Article  Google Scholar 

  33. Hoede, C., Bakker, R.: A Theory of Decisional Power. Journal of Mathematical Sociology 8, 309–322 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  34. Hu, X., Shapley, L.S.: On Authority Distributions in Organizations: Controls. Games and Economic Behavior 45, 153–170 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  35. Hu, X., Shapley, L.S.: On Authority Distributions in Organizations: Equilibrium. Games and Economic Behavior 45, 132–152 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  36. Jackson, M.O.: Social and Economic Networks. Princeton University Press, Princeton (2008)

    MATH  Google Scholar 

  37. Katz, L.: A New Status Index Derived from Sociometric Analysis. Psychometrika 18, 39–43 (1953)

    Article  MATH  Google Scholar 

  38. Rusinowska, A.: Different Approaches to Influence in Social Networks. Invited tutorial at the COMSOC 2010 (Third International Workshop on Computational Social Choice, Düsseldorf) (2010), http://ccc.cs.uni-duesseldorf.de/COMSOC-2010/slides/invited-rusinowska.pdf

  39. Rusinowska, A., de Swart, H.: Generalizing and Modifying the Hoede-Bakker Index. In: de Swart, H., Orłowska, E., Schmidt, G., Roubens, M. (eds.) TARSKI 2006. LNCS (LNAI), vol. 4342, pp. 60–88. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  40. Schmidt, G., Ströhlein, T.: Relations and Graphs, Discrete Mathematics for Computer Scientists. EATCS Monographs on Theoretical Computer Science. Springer, Heidelberg (1993)

    MATH  Google Scholar 

  41. Van den Brink, R., Gilles, R.: Measuring Domination in Directed Networks. Social Networks 22, 141–157 (2000)

    Article  Google Scholar 

  42. Van den Brink, R.: The Apex Power Measure for Directed Networks. Social Choice and Welfare 19, 845–867 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  43. Van den Brink, R., Borm, P., Hendrickx, R., Owen, G.: Characterization of the β-and the Degree Network Power Measure. Theory and Decision 64, 519–536 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  44. Wasserman, S., Faust, K.: Social Network Analysis: Methods and Applications. Cambridge University Press, Cambridge (1994)

    Book  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Centre d’Economie de la Sorbonne, Université Paris I Panthéon-Sorbonne, 106-112 Bd de l’Hôpital, 75647, Paris Cedex 13, France

    Agnieszka Rusinowska & Michel Grabisch

  2. Institut für Informatik, Universität Kiel, Olshausenstraße 40, 24098, Kiel, Germany

    Rudolf Berghammer

  3. Department of Philosophy, Erasmus University Rotterdam, P.O. Box 1738, 3000 DR, Rotterdam, The Netherlands

    Harrie De Swart

Authors
  1. Agnieszka Rusinowska
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  2. Rudolf Berghammer
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  3. Harrie De Swart
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  4. Michel Grabisch
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Editor information

Editors and Affiliations

  1. Faculty of Philosophy, Tilburg University, P.O. Box 90153, 5000, Tilburg, LE, The Netherlands

    Harrie de Swart

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Rusinowska, A., Berghammer, R., De Swart, H., Grabisch, M. (2011). Social Networks: Prestige, Centrality, and Influence. In: de Swart, H. (eds) Relational and Algebraic Methods in Computer Science. RAMICS 2011. Lecture Notes in Computer Science, vol 6663. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21070-9_2

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  • DOI: https://doi.org/10.1007/978-3-642-21070-9_2

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