Informative Missingness in Nominal Data: A Graph-Theoretic Approach to Revealing Hidden Structure

Missing data is often treated as a nuisance, routinely imputed or excluded from statistical analyses, especially in nominal datasets where its structure cannot be easily modeled. However, the form of missingness itself can reveal hidden relationships, substructures, and biological or operational constraints within a dataset. In this study, we present a graph-theoretic approach that reinterprets missing values not as gaps to be filled, but as informative signals. By representing nominal variables as nodes and encoding observed or missing associations as edges, we construct both weighted and unweighted bipartite graphs to analyze modularity, nestedness, and projection-based similarities. This framework enables downstream clustering and structural characterization of nominal data based on the topology of observed and missing associations; edge prediction via multiple imputation strategies is included as an optional downstream analysis to evaluate how well inferred values preserve the structure identified in the non-missing data. Across a series of biological, ecological, and social case studies, including proteomics data, the BeatAML drug screening dataset, ecological pollination networks, and HR analytics, we demonstrate that the structure of missing values can be highly informative. These configurations often reflect meaningful constraints and latent substructures, providing signals that help distinguish between data missing at random and not at random. When analyzed with appropriate graph-based tools, these patterns can be leveraged to improve the structural understanding of data and provide complementary signals for downstream tasks such as clustering and similarity analysis. Our findings support a conceptual shift: missing values are not merely analytical obstacles but valuable sources of insight that, when properly modeled, can enrich our understanding of complex nominal systems across domains.