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The dynamics of closeness and betweenness

  • Berno Buechel


    (Institute of Mathematical Economics, Bielefeld University)

  • Vincent Buskens


    (Department of Sociology, Utrecht University)

Although both betweenness and closeness centrality are claimed to be important for the effectiveness of someones network position, it has not been explicitly studied which networks emerge if actors follow incentives for these two positional advantages. We propose such a model and observe that network dynamics differ considerably in a scenario with either betweenness or closeness incentives compared to a scenario in which closeness and betweenness incentives are combined. Considering social consequences, we find low clustering when actors strive for either type of centrality. Surprisingly, actors striving for closeness are likely to reach networks with relatively low closeness and high betweenness, while this is the other way round for actors striving for betweenness. This shows that in both situations the network formation process implies a social dilemma in which the social optimum is not reached by individual optimizing.

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Paper provided by Center for Mathematical Economics, Bielefeld University in its series Center for Mathematical Economics Working Papers with number 398.

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Length: 35 pages
Date of creation: Jul 2008
Date of revision:
Handle: RePEc:bie:wpaper:398
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  1. Goyal, Sanjeev & Vega-Redondo, Fernando, 2007. "Structural holes in social networks," Journal of Economic Theory, Elsevier, vol. 137(1), pages 460-492, November.
  2. K. de Jaegher & J.J.A. Kamphorst, 2008. "Network formation with decreasing marginal benefits of information," Working Papers 08-16, Utrecht School of Economics.
  3. Venkatesh Bala & Sanjeev Goyal, 2000. "A Noncooperative Model of Network Formation," Econometrica, Econometric Society, vol. 68(5), pages 1181-1230, September.
  4. Sanjeev Goyal & Sumit Joshi, 2006. "Unequal connections," International Journal of Game Theory, Springer, vol. 34(3), pages 319-349, October.
  5. Dekker, D.J. & Franses, Ph.H.B.F. & Krackhardt, D., 2001. "An Equilibrium-Correction Model for Dynamic Network Data," ERIM Report Series Research in Management ERS-2001-39-MKT, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
  6. Berno Buechel, 2007. "Network formation with closeness incentives," Center for Mathematical Economics Working Papers 395, Center for Mathematical Economics, Bielefeld University.
  7. Matthew O. Jackson & Asher Wolinsky, 1995. "A Strategic Model of Social and Economic Networks," Discussion Papers 1098R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  8. Galeotti, Andrea & Goyal, Sanjeev & Kamphorst, Jurjen, 2006. "Network formation with heterogeneous players," Games and Economic Behavior, Elsevier, vol. 54(2), pages 353-372, February.
  9. Gert Sabidussi, 1966. "The centrality index of a graph," Psychometrika, Springer, vol. 31(4), pages 581-603, December.
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