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

  • Matthew O. Jackson


  • Brian W. Rogers


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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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
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  1. Jackson, Matthew O. & Rogers, Brian W., 2005. "The economics of small worlds," Working Papers 1214, California Institute of Technology, Division of the Humanities and Social Sciences.
  2. repec:tpr:qjecon:v:114:y:1999:i:3:p:739-767 is not listed on IDEAS
  3. Sanjeev Goyal & Marco van der Leij & Jose Luis Moraga, 2004. "Economics: An Emerging Small World?," Tinbergen Institute Discussion Papers 04-001/1, Tinbergen Institute.
  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. 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. Andrea Galeotti & Sanjeev Goyal & Jurjen Kamphorst, 2003. "Network Formation with Heterogeneous Players," Economics Discussion Papers 562, University of Essex, Department of Economics.
  7. 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.
  8. 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.
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