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Search in the formation of large networks: How random are socially generated networks?

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Author Info

  • Jackson, Matthew O.
  • Rogers, Brian W.

Abstract

We present a model of network formation where entering nodes find other nodes to link to both completely at random and through search of the neighborhoods of these randomly met nodes. We show that this model exhibits the full spectrum of features that have been found to characterize large socially generated networks. Moreover, we derive the distribution of degree (number of links) across nodes, and show that while the upper tail of the distribution is approximately ``scale- free,'' the lower tail may exhibit substantial curvature, just as in observed networks. We then fit the model to data from six networks. Besides offering a close fit of these diverse networks, the model allows us to impute the relative importance of search versus random attachment in link formation. We find that the fitted ratio of random meetings to search-based meetings varies dramatically across these applications. Finally, we show that as this random/search ratio varies, the resulting degree distributions can be completely ordered in the sense of second order stochastic dominance. This allows us to infer how the relative randomness in the formation process affects average utility in the network.

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Bibliographic Info

Paper provided by California Institute of Technology, Division of the Humanities and Social Sciences in its series Working Papers with number 1216.

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Length: 46 pages
Date of creation: Mar 2005
Date of revision:
Publication status: Published:
Handle: RePEc:clt:sswopa:1216

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Postal: Working Paper Assistant, Division of the Humanities and Social Sciences, 228-77, Caltech, Pasadena CA 91125
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Related research

Keywords: networks; network formation; power laws; scale-free networks; small worlds; search;

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References

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  1. Matthew O. Jackson & Brian W. Rogers, 2005. "The Economics of Small Worlds," Game Theory and Information 0503004, EconWPA.
  2. Andrea Galeotti & Sanjeev Goyal, 2002. "Network Formation with Heterogeneous Players," Tinbergen Institute Discussion Papers 02-069/1, Tinbergen Institute.
  3. 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.
  4. Dunia López-Pintado, 2004. "Diffusion In Complex Social Networks," Working Papers. Serie AD 2004-33, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  5. Xavier Gabaix, 1999. "Zipf'S Law For Cities: An Explanation," The Quarterly Journal of Economics, MIT Press, vol. 114(3), pages 739-767, August.
  6. Sanjeev Goyal & Marco J. van der Leij & Jos� Luis Moraga-Gonzalez, 2006. "Economics: An Emerging Small World," Journal of Political Economy, University of Chicago Press, vol. 114(2), pages 403-432, April.
  7. Barabási, Albert-László & Albert, Réka & Jeong, Hawoong, 2000. "Scale-free characteristics of random networks: the topology of the world-wide web," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 281(1), pages 69-77.
  8. Barabási, Albert-László & Albert, Réka & Jeong, Hawoong, 1999. "Mean-field theory for scale-free random networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 272(1), pages 173-187.
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Citations

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Cited by:
  1. Calvó-Armengol, Antoni & Patacchini, Eleonora & Zenou, Yves, 2005. "Peer Effects and Social Networks in Education and Crime," CEPR Discussion Papers 5244, C.E.P.R. Discussion Papers.
  2. Antoni Calvó-Armengol & Rahmi İlkılıç, 2009. "Pairwise-stability and Nash equilibria in network formation," International Journal of Game Theory, Springer, vol. 38(1), pages 51-79, March.
  3. Paolo Pin, 2006. "Eight degrees of separation," Working Papers 2006_26, Department of Economics, University of Venice "Ca' Foscari".
  4. Xavier Gabaix & Parameswaran Gopikrishnan & Vasiliki Plerou & H. Eugene Stanley, 2005. "Institutional Investors and Stock Market Volatility," NBER Working Papers 11722, National Bureau of Economic Research, Inc.
  5. Goeree, Jacob K. & Riedl, Arno & Ule, Aljaz, 2009. "In search of stars: Network formation among heterogeneous agents," Games and Economic Behavior, Elsevier, vol. 67(2), pages 445-466, November.
  6. Fernando Leiva B., 2006. "Pricing Patents through Citations," 2006 Meeting Papers 834, Society for Economic Dynamics.
  7. repec:hal:wpaper:halshs-00589657 is not listed on IDEAS
  8. Yannis M. Ioannides, 2005. "Random Graphs and Social Networks: An Economics Perspective," Discussion Papers Series, Department of Economics, Tufts University 0518, Department of Economics, Tufts University.

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