Recently, a developing interest has coincided between connectivity analysis in the neuroscience literature, and graphical modeling approaches in the statistical literature. The emergence of interest in these two domains has developed into a collaborative effect; an effort which tries to leverage the statistical methodologies used to estimate graphical models, and map them to analogous brain networks estimated from neuroscience data. The types of connectivity inferred between brain regions vary in their physiological and statistical interpretations, but in the functional MRI (fMRI) literature, two areas have emerged. In this thesis we focus on "functional" connectivity: a type of connectivity defined by interpreting networks as brain regions which covary in a similar fashion over some period of time. A refinement of this interpretation exists by instead examining brain regions which have a specified conditional independence structure over a period of time, and through this interpretation of functional connectivity approaches for graphical modeling can be applied. In this thesis we estimate temporal blocks with similar conditional independence behavior through the framework of Gaussian Graphical Models, and from these data jointly estimate the functional networks by using recently developed methods for joint graphical model estimation.