We present a method for the template-free characterization of binary superlattices. This is an extension of the Neighborhood Graph Analysis method, a technique which evaluates relationships between observed structures based on the topology of their first coordination shell [W. F. Reinhart, et al., Soft Matter, 2017, 13, 4733]. In the present work, we develop a framework for the analysis of multi-atom patterns, which incorporate structural information from the second coordination shell while providing a unified signature for all constituent particles in the superlattice. We construct an efficient metric for making quantitative comparisons between these patterns, making our algorithm the first capable of characterizing partial or defective superlattice structures. As in our previous work, we leverage machine learning techniques to characterize a range of self-assembled crystal structures, discovering a set of emergent collective variables which map each observed pattern into an intuitive global phase space. We demonstrate the method by performing classification of configurations from simulations of binary colloidal self-assembly in two dimensions.