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ssrn-id1739439 - Long-Run Integration in Social Networks...

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Electronic copy available at: http://ssrn.com/abstract=1739439 Long-Run Integration in Social Networks * Sergio Currarini Matthew O. Jackson Paolo Pin § This Draft: January 12, 2011 Abstract We study network formation where nodes are born sequentially and form links with pre- viously born nodes. Connections are formed through a combination of random meetings and through search, as in Jackson and Rogers (2007). A newborn’s random meetings of existing nodes are type-dependent and the newborn’s search is then by meeting the neighbors of the randomly met nodes. We study “long-run integration,” which requires that as a node ages sufficiently, the type distribution of the nodes connected to it approaches the overall type– distribution of the population. We show that long-run integration occurs if and only if the search part of the network formation process is unbiased, and that eventually the search process dominates in terms of the new links that an older node obtains. Integration, however, only oc- curs for sufficiently old nodes, and the aggregate type-distribution of connections in the network still reflects the bias of the random process. We illustrate the model with data on scientific citations in physics journals. 1 Introduction Homophily patterns in networks have important implications. For example, citation patterns across literatures can affect whether important ideas developed in one literature eventually diffuse into another. Homophily also affects a variety of behaviors and the welfare of individuals connected in social networks. 1 In this paper we analyze a model that provides new insight into patterns and the emergence of homophily, and illustrate its findings with an application to a network of scientific citations. * This supersedes “Overlapping Network Formation”, Currarini, Jackson and Pin (2006), which also appeared as a chapter in Pin’s dissertation in (2007). This version contains some new theoretical results and strengthening of the existing ones, and adds an empirical analysis of citations. Universit` a di Venezia. Email: [email protected] Department of Economics, Stanford University and the Santa Fe Institute. Email: [email protected], http://www.stanford.edu/ jacksonm/ § Dipartimento di Economia Politica, Universit´ a degli Studi di Siena (Italy). Email: [email protected] 1 See McPherson, Smith-Lovin, Cook (2001) and Jackson (2007, 2008) for more background and discussion. 1
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Electronic copy available at: http://ssrn.com/abstract=1739439 The primary issue that we investigate is how homophily patterns change over time. Do nodes become more integrated as they age? How does integration relate to the link formation process? For instance, does the network end up more integrated if new connections are found through the existing network or if nodes always meet anonymously? Intuition would suggest that the extent to which the existing connections influence new ones will seriously affect the long run behavior of the system.
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