The statistical analysis of import/export data is helpful to understand the mechanism that determines exchanges in an economic network. The probability of having a commercial relationship between two countries often depends on some unobservable (or not easy-to-measure) factors, like socio-economical conditions, political views, level of the infrastructures. To conduct inference on this type of data, we introduce a novel class of latent variable models for multiview networks, where a multivariate latent Gaussian variable determines the probabilistic behavior of the edges. We label our model the Graph Generalized Linear Latent Variable Model (GGLLVM) and we base our inference on the maximization of the Laplace-approximated likelihood. We call the resulting M-estimator the Graph Laplace-Approximated Maximum Likelihood Estimator (GLAMLE) and we study its statistical properties. Numerical experiments on simulated networks illustrate that the GLAMLE yields fast and accurate inference. A real data application to commodities trading in Central Europe countries unveils the import/export propensity that each node of the network has toward other nodes, along with additional information specific to each traded commodity.