This paper provides estimation methods for network formation models using observed data of a single large network. We characterize network formation as a simultaneous- move game with incomplete information and allow for the effects of indirect friends such as friends in common, so the utility from direct friends can be nonseparable. Nonsep-arability poses an challenge in the estimation because each individual then faces an interdependent multinomial discrete choice problem where the choice set increases with the number of individuals n. We propose a novel method to linearize the utility and derive the closed form of the conditional choice probability (CCP). With the closed form CCP, we show that the …nite-player game converges to some limiting game as n goes to in…nity. We propose a two-step estimation procedure using the equilibrium condition from the limiting game. The estimation procedure makes little assumption on equilibrium selection, is computationally simple, and provides consistent and asymptotic normal estimators for the structural parameters. Monte Carlo simulations show that the limiting game approximates …nite-player games well and can provide accurate estimates.