Applications of quantitative network analysis to functional brain connectivity have become popular in the last decade due to their ability to describe the general topological principles of brain networks. However, many issues arise when standard statistical analysis techniques are applied to functional magnetic resonance imaging (fMRI) connectivity maps. Frequently, summary measures of these maps, such as global efficiency and clustering coefficients, collapse the changing structures of graph topology from many scales to one. This can result in a loss of whole-brain spatio-temporal pattern information that may be significant in association and prediction analyses. Drawing from the electrical engineering field, the resistance perturbation distance is a quantification of similarity between graphs on the same vertex set that has been shown to identify changes in dynamic graphs, such as those from fMRI, while not being computationally expensive or result in a loss of information. This work proposes a novel kernel-based regression scheme that incorporates the resistance perturbation distance to better understand the association with biological phenotypes from fMRI using both simulated and real datasets.