Automatic Valet Parking (AVP) has garnered significant attention from industry and academia due to its potential to enhance traffic efficiency, parking safety, and user experience. While AVP technologies have been successfully applied in standard parking scenarios with clear markings, real-world parking environments are far more diverse and complex, posing challenges for current systems. To address these limitations, we present Parking-SG, an open-vocabulary hierarchical 3D scene graph representation, facilitating the application of AVP in open and complex environments. Our approach builds an object-based, open-vocabulary map that integrates both ground-level and ground-above objects for comprehensive environmental understanding. Leveraging common sense reasoning and object behavior relationships, various standard or non-standard parking spaces are inferred in open environments. Additionally, we extract and analyze path topology to construct a hierarchical map representation, supporting complex AVP tasks. Parking-SG is validated in both simulated and real-world environments, demonstrating its ability to generate rich environmental representations, accurately and flexibly infer parking spaces, and effectively perform complex AVP tasks.