This paper presents FloodRisk-Net, a novel unsupervised graph deep learning model for urban flood risk assessment in several US metropolitan areas. FloodRisk-Net identifies emerging flood risks by capturing spatial dependencies between regions and complex, nonlinear interactions between flood risk and urban features. Unlike existing flood risk assessment methods that focus solely on flood risk and exposure characteristics, FloodRisk-Net considers the interactions and spatial dependencies of various features to categorize cities into six flood risk levels. The model's interpretability enables feature analysis of areas within each flood risk level and identifies three archetypes that contribute to the highest flood risk within each metropolitan area. The analysis reveals a hierarchical spatial distribution of flood risk within each metropolitan area, with urban areas disproportionately bearing the highest flood risk. Furthermore, high overall flood risk levels and low spatial inequality across cities suggest limited options for balancing urban development and flood risk reduction. Finally, we discuss relevant flood risk reduction strategies that take into account the peak flood risk and the uneven spatial distribution of flood risk.