We present Structured Neural Radiance Field (Structured-NeRF) for indoor scene representaion based on a novel hierarchical scene graph structure to organize the neural radiance field. Existing object-centric methods focus only on the inherent characteristics of objects, while overlooking the semantic and physical relationships between them. Our scene graph is adept at managing the complex real-world correlation between objects within a scene, enabling functionality beyond novel view synthesis, such as scene re-arrangement. Based on the hierarchical structure, we introduce the optimization strategy based on semantic and physical relationships, thus simplifying the operations involved in scene editing and ensuring both efficiency and accuracy. Moreover, we conduct shadow rendering on objects to further intensify the realism of the rendered images. Experimental results demonstrate our structured representation not only achieves state-of-the-art (SOTA) performance in object-level and scene-level rendering, but also advances downstream applications in union with LLM/VLM, such as automatic and instruction/image conditioned scene re-arrangement, thereby extending the NeRF to interactive editing conveniently and controllably.