In the last 20 years network science has become an independent scientific field. We argue that by building network models network scientists are able to tame the vagueness of propositions about complex systems and networks, that is, to make these propositions precise. This makes it possible to study important vague properties such as modularity, near-decomposability, scale-freeness or being a small world. Using an epistemic model of network science, we systematically analyse the specific nature of network models and the logic behind (...) the taming mechanism. (shrink)