Topological methods provide us with measures of mesoscale, nonlinear organization in both structure and function of brain networks. Persistent homology, in particular, has been useful as a statistic for differentiation between populations and states. However, determining when two structures detected by topological means are similar -- homologous, in the non-mathematical sense -- remains a challenge. Here, I will discuss a new approach for comparing topological structure across modalities, subjects, or measurements; show initial results demonstrating their application to simulations of multi-system neural activity; and, discuss current and near-future challenges for applying topology to the study of brain networks.