We compare the nuclear energy generation rate and abundance levels given by an α-chain nuclear reaction network that contains only seven isotopes with a standard 13 isotope α-chain reaction network. The energy generation rate of these two small networks are also compared to the energy generation rate given by a 489 isotope reaction network with weak reactions turned on and off. The comparison between the seven isotope and α-chain reaction networks indicate the extent to which one can be replaced by the other, and the comparison with the 489 isotope reaction network roughly indicates under what physical conditions it is safe to use the seven isotope and α-chain reaction networks. The seven isotope reaction network reproduces the nuclear energy generation rate of the standard α-chain reaction network to within 30%, but often much better, during hydrostatic and explosive helium, carbon, and oxygen burning. It will also provide energy generation rates within 30% of an α-chain reaction network for silicon burning at densities less than 107 g cm-3. Provided there remains an equal number of protons and neutrons (Ye=0.5) over the course of the evolution, and that flows through α-particle channels dominate, then both of the small reaction networks return energy generation rates that are compatible with the energy generation rate returned by the 489 reaction network. If Ye is significantly different from 0.5, or if there are substantial flows through neutron and protons channels, then it is not generally safe to employ any α-chain based reaction network. The relative accuracy of the seven isotope reaction network, combined with its reduction in the computational cost, suggest that it is a suitable replacement for α-chain reaction networks for parameter space surveys of a wide class of multidimensional stellar models.