In the following article, we provide an exposition of exact computational methods to perform parameter inference from partially observed network models. In particular, we consider the duplication attachment model that has a likelihood function that typically cannot be evaluated in any reasonable computational time. We consider a number of importance sampling (IS) and sequential Monte Carlo (SMC) methods for approximating the likelihood of the network model for a fixed parameter value. It is well-known that, for IS, the relative variance of the likelihood estimate typically grows at an exponential rate in the time parameter (here this is associated with the size of the network); we prove that, under assumptions, the SMC method will have relative variance that can grow only polynomially. In order to perform parameter estimation, we develop particle Markov chain Monte Carlo algorithms to perform Bayesian inference. Such algorithms use the aforementioned SMC algorithms within the transition dynamics. The approaches are illustrated numerically. © Mary Ann Liebert, Inc.