The application of data-driven models for rapid static security analysis in new power system is a research area worth exploring. Enhancing the generalization ability of data-driven models to operation condition changes and the adaptability to power system topology variations is one of the key technical challenges. A graph learning model for static security analysis of the power system based on power flow embedding and the min-cut pooling is proposed. At first, a power flow embedding module directed by the node voltage restoration is designed to improve the model's generalization ability, which converts the topological differences in N-1 contingency scenarios into node feature differences. Secondly, based on the concept of community partitioning, a min-cut pooling technology is employed to dynamically reduce node scale and node feature dimensions, which enables the model to adapt to topological changes. Verification tests and visualization analyses conducted on IEEE 39-bus and IEEE 118-bus systems demonstrate that the model can achieve high accuracy, second-level evaluation speed, and good adaptability to variation of the power grid scale and topology.