Long-Run Integration in Social Networks

We study network formation where nodes are born sequentially and form links with previously 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 occurs 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