For disaster response systems in smart cities, robust and adaptable frameworks are required to effectively manage unforeseen events. This study introduces a novel graph-based disaster response framework based on IoT, AI, and cloud technologies. The system is designed against formally defined quality objectives drawn from ISO/IEC 25010:2023, including performance efficiency (\(ADE \ge 0.8\)), reliability (\(DSHM \ge 0.5\), \(DDI \ge 0.7\)), and maintainability (\(DSR \ge 0.5\)), providing designers with measurable acceptance thresholds for architectural validation. This framework models the components of disaster response (sensors, gateways, decision layers, and actuators) using a novel graph scheme that offers an intuitive way to examine interactions and dependencies. On this graph, we consider various design quality metrics (complexity of disaster detection, severity identification, type identification, sensing complexity, data integrity, monitoring sensor health, alert dissemination efficiency, recoverability of the system, and component reusability) useful in making quantitative assessments of the framework. We conduct an extensive evaluation through a practical flood response case in Pakistan to illustrate the usefulness of the metrics for elaborating on resource allocation, improving decision-making, and generating time-sensitive alerts. The findings illustrate high efficiency for the framework (ADE of 0.833 in the evaluated scenario, with dissemination efficiency ranging from 0.83 to 0.91 across configurations) and resilience (DSR ranging from 0.4 to 0.875 across regions, with best-case recoverability of 0.875 in stable regions). This work creates a tangible and powerful linkage between theoretical abstractions of models and practical applications by providing a structured, measurable, and scalable approach that policymakers and designers can adopt to develop disaster management supports for smart cities.