The evolution of sex determination mechanisms is known to be relatively rapid, though recent evidence indicates that certain parts of the mechanism may be more highly conserved. These characteristics establish the sex determination mechanism as a good candidate for the theoretical study of gene network evolution, particularly of networks involved in development. We investigate the short-term evolutionary potential of the sex determination mechanism in Drosophila melanogaster with the aid of a synchronous logical model. We introduce general theoretical concepts such as a network-specific form of mutation, and a notion of functional equivalence between networks. We apply this theoretical framework to the sex determination mechanism and compare it to a population of random networks, enabling us to find features both general to sex determination networks, and particular to the Drosophila network. In general, sex determination networks exist within large sets of functionally equivalent networks all of which satisfy the sex determination task. These large sets are in turn composed of subsets which are mutationally related, suggesting a high degree of flexibility is available without compromising the core functionality. Two particular characteristics of the Drosophila network are found: (a) a parsimonious use of gene interactions, and (b) the network structure can produce a relatively large number of dynamical pattern variations through single network mutations.