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Business Models on the Web is Michael Rappa's definitive article on the subject. Rappa is the Alan T. Dickson Distinguished University Professor of Technology Management at North Carolina State University, where he specializes in the study of e-commerce and the assessment of emerging technologies.
Graph theory lets us draw some intuitively powerful pictures of how we understand our businesses and the relationships among the various 'players' within the 'game'. But underlying the intuitive simplicity of these evocative pictures, graph theory also provides a rigorous method for deciding what models can be built and how the pieces can be put together.
Meta Modelling: When you apply graph theory to model-making you start slipping into some deep weeds; meta-modeling. Meta-models are models about models; models that define what kinds of specific models can be constructed from the elements allowed in the specific model's construction.
We use Open Source object technologies in the Sohodojo TechSIG to create software frameworks which implement role-based executable business models. So we have to think rigorously and practically about meta-model issues. Unless you are interested in working on the development of such technologies, you shouldn't have to worry too much about meta-model issues. The model-based tools you choose to build your web-based business will be either an explicit or implicit selection of your preferred meta-model. That is, you can't expect any one tool to build all kinds of models. So the tool developer has made a design choice in building a tool to support a particular meta-model.