  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 nodes' neighborhoods
approaches the global type distribution, provided that the network-based search
is unbiased. However, younger nodes' 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.
