The ability to simulate realistic networks based on empirical data is an important task across scientific disciplines, from epidemiology to computer science. Often simulation approaches involve selecting a suitable network generative model such as Erdös-Rényi or small-world. However, few tools are available to quantify if a particular generative model is suitable for capturing a given network structure or organization. We utilize advances in interpretable machine learning to classify simulated networks by our generative models based on various network attributes, using both primary features and their interactions. Our study underscores the significance of specific network features and their interactions in distinguishing generative models, comprehending complex network structures, and the formation of real-world networks.