Search in the Formation of Large Networks: How Random are Socially Generated Networks?
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.
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Matthew O. Jackson & Asher Wolinsky, 1994.
"A Strategic Model of Social and Economic Networks,"
1098, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Jackson, Matthew O. & Rogers, Brian W., 2005.
"The economics of small worlds,"
1214, California Institute of Technology, Division of the Humanities and Social Sciences.
- Xavier Gabaix, 1999. "Zipf'S Law For Cities: An Explanation," The Quarterly Journal of Economics, MIT Press, vol. 114(3), pages 739-767, August.
- Sanjeev Goyal & Marco van der Leij & José Luis Moraga-Gonzàlez, 2004.
"Economics: An Emerging Small World?,"
2004.84, Fondazione Eni Enrico Mattei.
- 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.
- Galeotti, Andrea & Goyal, Sanjeev & Kamphorst, Jurjen, 2006.
"Network formation with heterogeneous players,"
Games and Economic Behavior,
Elsevier, vol. 54(2), pages 353-372, February.
- López-Pintado, Dunia, 2008.
"Diffusion in complex social networks,"
Games and Economic Behavior,
Elsevier, vol. 62(2), pages 573-590, March.
- 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.
When requesting a correction, please mention this item's handle: RePEc:wpa:wuwpga:0503005. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (EconWPA)
If references are entirely missing, you can add them using this form.