A natural degree preserving mutation operator consists in a choice of two edges e = xy and f = uv, cut both edges, and re-attaches the vertices as e ′ = xu and f ′ = yv. Clearly, vertex degree is preserved. The operator can also be used as a way to model simple elimination reactions, since CH CCl can yield C C plus HCl. However, in cases where the resulting molecule is disconnected, the reattachment of edges necessarily produces isomers, i.e., does not change the chemical composition. This kind of edge-swap operation was recently used in models for the evolution of population structures .