We have accumulated a large amount of biological network data and expect even more to come. Soon, we anticipate being able to compare many different biological networks as we commonly do for molecular sequences. It has long been believed that many of these networks change, or rewire, at different rates. It is therefore important to develop a framework to quantify the differences between networks in a unified fashion. We developed such a formalism based on analogy to simple models of sequence evolution, and used it to conduct a systematic study of network rewiring on all the currently available biological networks. We found that, similar to sequences, biological networks show a decreased rate of change at large time divergences, because of saturation in potential substitutions. However, different types of biological networks consistently rewire at different rates. Using comparative genomics and proteomics data, we found a consistent ordering of the rewiring rates: transcription regulatory, phosphorylation regulatory, genetic interaction, miRNA regulatory, protein interaction, and metabolic pathway network, from fast to slow. This ordering was found in all comparisons we did of matched networks between organisms. To gain further intuition on network rewiring, we compared our observed rewirings with those obtained from simulation. We also investigated how readily our formalism could be mapped to other network contexts, in particular, we showed how it could be applied to analyze changes in a range of commonplace networks such as family trees, co-authorships and linux-kernel function dependencies.