We use a Toy Model of chemistry that represents molecules in terms of usual structural formulae to generate large chemical reaction networks. An extremely simplified quantum mechanical energy calculation and a straightforward implementation of reactions as graph rewritings ensure both transparency and closeness to chemical reality, both conditions that are necessary for the analysis of generic properties of large reaction networks. We show that some chemical networks graphs, e.g., repetitive Diels-Alder reactions, have the small-world property and exhibit a scale-free degree distribution. On the other hand, the Formose reaction does not fit well to this paradigm.