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Applying relational algebra and RelView to measures in a social network

Author

Listed:
  • Rudolf Berghammer

    (Institut für Informatik - CAU - Christian-Albrechts-Universität zu Kiel = Christian-Albrechts University of Kiel = Université Christian-Albrechts de Kiel)

  • Agnieszka Rusinowska

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Harrie de Swart

    (Faculteit Wijsbegeerte-Logica en taalanalyse - Tilburg University [Netherlands])

Abstract

We present an application of relation algebra to measure agents' 'strength' in a social network with influence between agents. In particular, we deal with power, success, and influence of an agent as measured by the generalized Hoede-Bakker index and its modifications, and by the influence indices. We also apply relation algebra to determine followers of a coalition and the kernel of an influence function. This leads to specifications, which can be executed with the help of the BDD-based tool RelView after a simple translation into the tool's programming language. As an example we consider the present Dutch parliament.

Suggested Citation

  • Rudolf Berghammer & Agnieszka Rusinowska & Harrie de Swart, 2010. "Applying relational algebra and RelView to measures in a social network," Post-Print hal-00515878, HAL.
    • Handle: RePEc:hal:journl:hal-00515878
    DOI: 10.1016/j.ejor.2009.05.020
    Note: View the original document on HAL open archive server: https://hal.science/hal-00515878
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    References listed on IDEAS

    as
    1. Michel Grabisch & Agnieszka Rusinowska, 2010. "A model of influence in a social network," Theory and Decision, Springer, vol. 69(1), pages 69-96, July.
    2. Berghammer, Rudolf & Rusinowska, Agnieszka & de Swart, Harrie, 2007. "Applying relational algebra and RelView to coalition formation," European Journal of Operational Research, Elsevier, vol. 178(2), pages 530-542, April.
    3. Agnieszka Rusinowska & Harrie de Swart & Jan-Willem van der Rijt, 2005. "A new model of coalition formation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 24(1), pages 129-154, September.
    4. Berghammer, Rudolf & Rusinowska, Agnieszka & de Swart, Harrie, 2009. "An interdisciplinary approach to coalition formation," European Journal of Operational Research, Elsevier, vol. 195(2), pages 487-496, June.
    5. Dennis Leech, 2003. "Computing Power Indices for Large Voting Games," Management Science, INFORMS, vol. 49(6), pages 831-837, June.
    6. Dan S. Felsenthal & Moshé Machover, 1998. "The Measurement of Voting Power," Books, Edward Elgar Publishing, number 1489.
    7. Laruelle, Annick & Widgren, Mika, 1998. "Is the Allocation of Voting Power among EU States Fair?," Public Choice, Springer, vol. 94(3-4), pages 317-339, March.
    8. Algaba, E. & Bilbao, J.M. & Fernandez, J.R., 2007. "The distribution of power in the European Constitution," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1752-1766, February.
    9. Shapley, L. S. & Shubik, Martin, 1954. "A Method for Evaluating the Distribution of Power in a Committee System," American Political Science Review, Cambridge University Press, vol. 48(3), pages 787-792, September.
    10. Rae, Douglas W., 1969. "Decision-Rules and Individual Values in Constitutional Choice," American Political Science Review, Cambridge University Press, vol. 63(1), pages 40-56, March.
    11. Crama, Yves & Leruth, Luc, 2007. "Control and voting power in corporate networks: Concepts and computational aspects," European Journal of Operational Research, Elsevier, vol. 178(3), pages 879-893, May.
    12. Alonso-Meijide, J.M. & Casas-Mendez, B. & Holler, M.J. & Lorenzo-Freire, S., 2008. "Computing power indices: Multilinear extensions and new characterizations," European Journal of Operational Research, Elsevier, vol. 188(2), pages 540-554, July.
    13. Harrie de Swart & Agnieszka Rusinowska, 2007. "On some properties of the Hoede-Bakker index," Post-Print halshs-00201414, HAL.
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    Cited by:

    1. Berghammer, Rudolf & Rusinowska, Agnieszka & de Swart, Harrie, 2013. "Computing tournament solutions using relation algebra and RelView," European Journal of Operational Research, Elsevier, vol. 226(3), pages 636-645.
    2. Berghammer, Rudolf & Bolus, Stefan & Rusinowska, Agnieszka & de Swart, Harrie, 2011. "A relation-algebraic approach to simple games," European Journal of Operational Research, Elsevier, vol. 210(1), pages 68-80, April.
    3. Agnieszka Rusinowska & Rudolf Berghammer & Harrie de Swart & Michel Grabisch, 2011. "Social networks: Prestige, centrality, and influence (Invited paper)," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00633859, HAL.
    4. Castro, Jordi & Nasini, Stefano, 2015. "Mathematical programming approaches for classes of random network problems," European Journal of Operational Research, Elsevier, vol. 245(2), pages 402-414.
    5. Schneider, Kellie & Rainwater, Chase & Pohl, Ed & Hernandez, Ivan & Ramirez-Marquez, Jose Emmanuel, 2013. "Social network analysis via multi-state reliability and conditional influence models," Reliability Engineering and System Safety, Elsevier, vol. 109(C), pages 99-109.
    6. Berghammer, Rudolf & Bolus, Stefan, 2012. "On the use of binary decision diagrams for solving problems on simple games," European Journal of Operational Research, Elsevier, vol. 222(3), pages 529-541.
    7. repec:hal:wpaper:hal-00756696 is not listed on IDEAS

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    More about this item

    Keywords

    RelView; relation algebra; social network; Hoede-Bakker index; influence index;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C88 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Other Computer Software
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation

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