In what follows, I discuss the semantic view of theories, specifically in the ‘state space’ formulation that has been developed by Bas van Fraassen, Frederick Suppe, and others and applied by Elisabeth Lloyd. I consider the claims that the state space view makes about how scientific theories are best understood. I then discuss a particular model from network theory, the alpha-model developed by Duncan Watts, and try to apply the state space view to the alpha-model theory. I argue that the way Watts uses the alpha-model is not described very easily under the state space approach, because its parameters are idealized in a way that the state space approach does not account for, and because the relation between the alpha-model and the world is not one of statistical fit between its models and data.