Interactions among biological entities contain more information than purely the similarities between the entities. For example, interactions between genes, and gene products, can be more informative than the sequence similarities of the genes involved. However, the study of biological networks and their evolution in particular is still in its infancy. Simplified theoretical models of the development of biological networks from a starting state exist, but the problem of finding a distance between existing biological networks, with an unknown history, has seen less research. Metrics for network distance can also be used to measure the fit between theoretically derived networks and their real-world counterpart. In this article, we present a useful model of biological network distance and demonstrate an implementation using simulated gene regulatory networks. We compared our method with existing methods for network alignment and showed that we are much better able to identify evolutionary changes in biological networks. In particular, we can recover the evolutionary trees that describe the relationship between these networks.