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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Sanjeev Goyal & Marco J. van der Leij & José Luis Moraga-Gonzalez, 2006.
"Economics: An Emerging Small World,"
Journal of Political Economy,
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Other versions:
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.
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Cited by: (explanations, 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.)
Paolo Pin, 2006.
"Eight degrees of separation,"
Working Papers
2006_26, University of Venice "Ca' Foscari", Department of Economics.
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Jackson, Matthew O. & Yariv, Leeat, .
"Diffusion on social networks,"
Working Papers
1251, California Institute of Technology, Division of the Humanities and Social Sciences.
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