This paper develops a tractable endogenous network formation model of the interbank market. Due to liquidity shocks, banks face a trade-off between investing their resources in a liquid asset and a high-yield illiquid asset. The interbank market is modeled as a network. A link extended by one bank to another is interpreted as a credit line from which the former bank can borrow a share of the latter s liquid assets to cover liquidity outflows. The central bank, by means of its standing facilities, lends resources to banks that are short in liquidity and borrows from institutions with liquidity surpluses at predetermined rates. These rates establish a corridor in which the rate that banks charge for interbank loans must lie. In this setting, we characterize the unique equilibrium of banks liquidity holdings for any network. We then endogenize the network, via banks decision of credit lines, and provide a sharp equilibrium characterization: every equilibrium network is a complete core-periphery graph. This characterization is consistent with empirically observed networks. Moreover, we introduce a trade-off for central banks when choosing the corridor rate: a narrower corridor implies more precise targeting of the interbank rate, which is important for the conduct of monetary policy. However, if we account for banks linking decisions, this may lead to an equilibrium with a sparser network, where total liquidity holdings are higher, incurring an implicit cost since these funds could be invested in the more productive illiquid asset instead. More generally, our analysis highlights the important role that endogenous networks play in the transmission of monetary policy.