In contrast to crossover on string representations, cut-and-join crossover on graphs is surprisingly versatile. In particular, we have shown that every finite graph with fixed maximal degree can be constructed by a GA operating on a finite size population within a finite number of steps. Moreover, the search space of such graphs is strongly connected. Taken together, therefore, the natural or degree-preserving cut-and-join crossover operations, possibly complemented by edge-swapping as a simple mutation operator, are sufficient to give access to any molecular scaffold. The natural and degree-preserving cutand-join crossover conceptually resembles chemical reactions that exchange (large) moieties between pairs of molecules. Such exchanges appear to be particularly prevalent in metabolic networks. Our results on reachability and connectedness of chemical space under cut-and-join crossover thus suggests that metabolic reactions might also be capable of reaching all of chemical space. It is worth noting in this context that if a natural join