Urban flood risk emerges from complex and nonlinear interactions among multiple features related to flood hazard, flood exposure, and social and physical vulnerabilities, along with the complex spatial flood dependence relationships. Existing approaches for characterizing urban flood risk, however, are primarily based on flood plain maps, focusing on a limited number of features, primarily hazard and exposure features, without consideration of feature interactions or the dependence relationships among spatial areas. To address this gap, this study presents an integrated urban flood-risk rating model based on a novel unsupervised graph deep learning model (called FloodRisk-Net). FloodRisk-Net is capable of capturing spatial dependence among areas and complex and nonlinear interactions among flood hazards and urban features for specifying emergent flood risk. Using data from multiple metropolitan statistical areas (MSAs) in the United States, the model characterizes their flood risk into six distinct city-specific levels. The model is interpretable and enables feature analysis of areas within each flood-risk level, allowing for the identification of the three archetypes shaping the highest flood risk within each MSA. Flood risk is found to be spatially distributed in a hierarchical structure within each MSA, where the core city disproportionately bears the highest flood risk. Multiple cities are found to have high overall flood-risk levels and low spatial inequality, indicating limited options for balancing urban development and flood-risk reduction. Relevant flood-risk reduction strategies are discussed considering ways that the highest flood risk and uneven spatial distribution of flood risk are formed.

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