As the products become more and more complex, it is very difficult for the quality analysis of the complex products. In order to facilitate analysis, complex products are usually divided into several zones reasonably. Products arranged in the same zone usually have some spatial correlation which can't be found in design stage until the operation stage, which usually has damage to the quality of products. Hence, it is important to express the correlation among products in the same zone accurately and clearly. However, the traditional physical models cannot express the correlation among products clearly. Although a product's function structure can be effectively and clearly described by using generalized directed graph (GDG) theory, it can't express the correlation between function and environment. In this paper, we extend generalized directed graph theory first, adding color and shape elements to express the information clearly. Then the modeling method of function structure is proposed for zonal products by using improved generalized directed graph (IGDG). Finally, a power screwdriver is modeled as an example. Comparing with the results of GDG, we can find that the correlation between function and environment can be expressed clearly by using IGDG. This provides effective information for the designers in the design and layout stage, avoiding the damage of the correlation on the quality of the zonal products.