This paper provides a novel approach to identification and estimation of a network formation model using observed network data, where the model acknowledges possible externalities in agents' utilities of forming connections with one another. The existence of externalities induces an issue of multiple equilibria. We first show that local point identification of the parameters of interest is possible under a mild assumption on the equilibrium selection process. We then propose a Bayesian estimation method to conduct statistical inference of structural payoff coefficients. Implementing the resulting MCMC algorithm requires sampling from the generalized inverse normal distribution, for which we found no efficient sampling algorithm in the literature. A by-product of this paper is to provide such efficient sampling algorithm for the regular and truncated variants of this distribution. Our method also allows us to estimate equilibrium selection probabilities, which requires knowledge on possible equilibrium configurations. We address this issue by proposing a composite likelihood function based on subgraphs of the observed network. We show that the use of a composite likelihood induces misspecification, characterize the Kullback-Leibler divergence that measures this misspecification error and show this measure can be used to tune the composite likelihood weights. We present an empirical application to model the network formation process of individuals creating social connections in villages in Karnataka, India and find strong evidence of homophily effects.