This paper addresses the issue of estimating structural models on data from a single network. For example, in Macroeconomics, one could use the production network of the US. This is a longstanding problem in economics and related fields. While there exist methods for estimating structural models on many graphs/networks, there is limited research on a general-purpose algorithm to fit structural models on a single network. This study proposes an algorithm adapted from Deep Learning, dubbed Sequential Neural Posterior Estimation (SNPE), for network analysis, which enables Bayesian and likelihood estimation of arbitrary structural models, given standard conditions. SNPE is a simulation-based estimator, which can produce likelihoods via samples from a distribution. Networks sampled from a model are converted to numerical statistics, which hopefully are sufficient, via graph neural networks and other methods. Simulated tests demonstrate the effectiveness and accuracy of this approach. To demonstrate the capability of this model, the algorithm is applied to estimate a homophily citation model (Bramoulle et. al. 2012) on empirical data, which was not attempted by the original paper. This study presents a promising algorithm for fitting structural models on a single network, opening avenues for future research in network estimation.