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Search in the Formation of Large Networks: How Random are Socially Generated Networks?

  • Matthew O. Jackson

    (Caltech)

  • Brian W. Rogers

    (Caltech)

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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File URL: http://econwpa.repec.org/eps/game/papers/0503/0503005.pdf
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Paper provided by EconWPA in its series Game Theory and Information with number 0503005.

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Length: 44 pages
Date of creation: 14 Mar 2005
Date of revision:
Handle: RePEc:wpa:wuwpga:0503005
Note: Type of Document - pdf; pages: 44
Contact details of provider: Web page: http://econwpa.repec.org

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  1. Galeotti, Andrea & Goyal, Sanjeev & Kamphorst, Jurjen, 2006. "Network formation with heterogeneous players," Games and Economic Behavior, Elsevier, vol. 54(2), pages 353-372, February.
  2. 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.
  3. Matthew O. Jackson & Brian W. Rogers, 2005. "The Economics of Small Worlds," Journal of the European Economic Association, MIT Press, vol. 3(2-3), pages 617-627, 04/05.
  4. 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.
  5. 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.
  6. 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.
  7. López-Pintado, Dunia, 2008. "Diffusion in complex social networks," Games and Economic Behavior, Elsevier, vol. 62(2), pages 573-590, March.
  8. Xavier Gabaix, 1999. "Zipf'S Law For Cities: An Explanation," The Quarterly Journal of Economics, MIT Press, vol. 114(3), pages 739-767, August.
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