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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.

(This abstract was borrowed from another version of this item.)

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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
Phone: 626 395-4065
Fax: 626 405-9841
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Web page: http://www.hss.caltech.edu/ss

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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. Sanjeev Goyal & Marco van der Leij & José Luis Moraga Gonzales, 2004. "Economics: An Emerging Small World?," CESifo Working Paper Series 1287, CESifo Group Munich.
  2. Andrea Galeotti & Sanjeev Goyal & Jurjen Kamphorst, 2003. "Network Formation with Heterogeneous Players," Economics Discussion Papers 562, University of Essex, Department of Economics.
  3. 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.
  4. Matthew O. Jackson & Brian W. Rogers, 2005. "The Economics of Small Worlds," Game Theory and Information 0503004, EconWPA.
  5. Dunia López-Pintado, 2004. "Diffusion In Complex Social Networks," Working Papers. Serie AD 2004-33, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  6. Jackson, Matthew O. & Wolinsky, Asher, 1996. "A Strategic Model of Social and Economic Networks," Journal of Economic Theory, Elsevier, vol. 71(1), pages 44-74, October.
  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. 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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Citations

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Cited by:
  1. Aljaž Ule & Jacob K. Goeree & Arno Riedl, 2007. "In Search of Stars: Network Formation among Heterogeneous Agents," Working Papers 2007.65, Fondazione Eni Enrico Mattei.
  2. 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.
  3. Antoni Calvó-Armengol & Rahmi Ilkiliç, 2004. "Pairwise-Stability and Nash Equilibria in Network Formation," Working Papers 182, Barcelona Graduate School of Economics.
  4. Gabrielle Demange, 2011. "On the influence of rankings," Working Papers halshs-00589657, HAL.
  5. Fernando Leiva B., 2006. "Pricing Patents through Citations," 2006 Meeting Papers 834, Society for Economic Dynamics.
  6. Pin, Paolo, 2011. "Eight degrees of separation," Research in Economics, Elsevier, vol. 65(3), pages 259-270, September.
  7. Goeree,Jacob K. & Riedl,Arno & Ule,Aljaz, 2005. "In Search of Stars: Network Formation among Heterogeneous Agents," Research Memorandum 032, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  8. 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.
  9. 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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