Abstract
We model network formation when heterogeneous nodes enter sequentially and form connections through both random meetings and network-based search, but with type-dependent biases. We show that there is “long-run integration”, whereby the composition of types in sufficiently old nodesʼ neighborhoods approaches the global type-distribution, provided that the network-based search is unbiased. However, younger nodesʼ connections still reflect the biased meetings process. We derive the type-based degree distributions and group-level homophily patterns when there are two types and location-based biases. Finally, we illustrate aspects of the model with an empirical application to data on citations in physics journals.
Highlights
Do nodes become more integrated or more segregated as they age? How does this evolution depend on the link formation process? In particular, does the network become more integrated if new connections are formed at random or if they are formed through the existing network?
We find that the proportion of citations that a paper obtains from other papers in its own field decreases as the paper ages and becomes more cited
This paper contributes to our understanding of how heterogeneity and homophily among individuals impact the networks that they form
Summary
Patterns in networks have important consequences. For example, citations across literatures can affect whether, and how quickly, ideas developed in one field diffuse into another. Weak integration is satisfied whenever the probability that a given node is found increases with that node’s degree This holds in any version of our model where at least some links are formed through search and there is some possibility of connecting across types. We derive an explicit formula relating a node’s local homophily among neighbors to its age or degree This illustrates our general results and further shows how partial and long-run integration are affected by changes in types’ shares. We study two important structural properties of the resulting network that are less tractable in the general model: degree distributions and group-level homophily. The observed citation patterns provide some evidence of the partial integration property and are at least partly consistent search follows a less biased (possibly unbiased) pattern in the citation process In studying this application we are motivated by two factors.
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