This study investigates the internal structure of the Habitat and Riparian Health Index (HRI) by identifying conditional dependencies among its components and the mechanisms that form grade boundaries, rather than treating HRI as a simple arithmetic sum. Using the 2024 national river assessment dataset, the analysis combined bootstrap-supported Bayesian Networks for stable dependency inference with classification decision trees for explicit grading rules and threshold identification. A multi-criterion priority scheme integrating network centrality, contribution to total-score variability, and classification contribution was also applied to derive management priorities within and across basins. Across all basins and analytical perspectives, Flow Velocity Diversity consistently emerged as the most influential component. It occupied the central position in the dependency structure and accounted for the largest share of variability in the composite score, indicating that it operates as a system-level outcome in which channel morphology, bed condition, and anthropogenic constraints converge. The grading mechanism was strongly asymmetric. Deficiencies in riverbank protection functioned as a dominant trigger for rapid grade deterioration, whereas attainment of the highest grade required a conjunctive and non-linear pathway in which sufficient flow heterogeneity was accompanied by the sequential resolution of structural constraints, particularly those associated with transverse structures and embankments. Basin-level comparisons further showed that network structures were not interchangeable, with the Nakdong River basin exhibiting the most distinct configuration and basinspecific priority patterns. These results imply that management should separate strategies aimed at preventing degradation through bottleneck control from strategies aimed at achieving top-tier conditions through coordinated, multi-component interventions.