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Evolved from our engineering experience, this paper presents a mathematical framework to define and analyze an SOA (service-oriented architecture) model. SOA model, composed by design elements, is represented as directed graph based on graph theory. For each design element, two directed graphs are created to reflect the panoramic view and relationships of this design element with other design elements of same model, and used for impact and completion analysis of this design element. A numerical value called the relative importance indicator is computed to quantify the relationship between any two design elements. This indicator forms a matrix that is used as a base for more advanced analysis, such as model partition, model coupling, and variation-oriented design. Some future research directions such as model reduction are discussed at the end of this paper.