Network modeling is critical and central to the study of complex systems. Modeling enables researchers to examine emergent behavior and related phenomena from the milieu of interacting patterns at the local level. These complex systems are diverse, ranging from the global economy, neuroscience, protein folding molecular interactions, to the Internet. Evaluating network models on their ability to automatically learn the underlying features is integral to algorithm development in many areas of computational science. Here we describe methods and develop algorithms that extend and evaluate hyperedge replacement grammars, a formalism in formal language theory. We detail extensions for model-inference on real-world networks and graph generation. Discovering patterns involved in system behavior to build models for real-world systems that preserve many of the network properties during the generation step is the central focus of this work. Growing similar structures at various scale is also crucial to the evolution of the scientific tools required in today's information landscape. Experimental results demonstrate that hyperedge replacement grammars offer a new way to learn network features that facilitate compelling graphical structure generation that advances network science in areas of modeling and network analysis.