The study of complex brain networks, where structural or functional connections are evaluated to create an interconnected representation of the brain, has grown tremendously over the past decade. Much of the statistical network science tools for analyzing brain networks have been developed for cross-sectional studies and for the analysis of static networks. However, with both an increase in longitudinal study designs, as well as an increased interest in the neurological network changes that occur during the progression of a disease, sophisticated methods for longitudinal brain network analysis are needed. We propose a paradigm for longitudinal brain network analysis over patient cohorts, with the key challenge being the adaptation of Stochastic Actor-Oriented Models (SAOMs) to the neuroscience setting. SAOMs are designed to capture network dynamics representing a variety of influences on network change in a continuous-time Markov chain framework. Network dynamics are characterized through both endogenous (i.e., network related) and exogenous effects, where the latter include mechanisms conjectured in the literature. We outline an application to the resting-state fMRI setting with data from the Alzheimers Disease Neuroimaging Initiative (ADNI) study. We draw illustrative conclusions at the subject level and make a comparison between elderly controls and individuals with AD.