This paper studies a search-based model of OTC markets in which clients with heterogenous trading needs direct their trades to one of ex-ante identical dealers. The main insight of the paper is that the way clients sort across dealers shapes dealer-to-dealer trading patterns and, in turn, generates a core-periphery interdealer network structure. Dealers in the model become heterogeneous because they attract different clients in equilibrium. Some dealers attract clients who trade frequently (e.g., index funds); others attract clients with infrequent trading needs (e.g., pension funds). Dealers attracting clients with frequent trading needs receive a larger volume of client orders, trade more with other dealers, and, as a result, form the core of the interdealer network. Conversely, dealers specializing in clients with infrequent trading needs form the periphery. I also show that accounting for client heterogeneity across dealers (a) challenges standard measurements and interpretations of bid-ask spreads and (b) generates predictions on bid-ask spreads and dealer centrality consistent with the empirical literature.