Functional connectivity (FC) has been extensively used to study functional associations among pairs of brain regions and identify temporal correlations between neurophysiological events. Graph theoretic methods have been implemented to model the FC using data collected the functional magnetic resonance imaging technology. Specifically, since FC refers to the estimation of undirected temporal associations between any two regions in the brain, often including spatially incongruous areas, a graph with vertices corresponding to brain regions of interest and edges corresponding to existing connections between regions can be used as a model for FC. In this talk, I will review various approaches to FC estimation using graph theoretic approaches and propose a novel estimation procedure incorporating structural connectivity information estimated by diffusion tensor imaging. I will show that the proposed approach results in improved inference of estimation of the graph and computational efficiency. I will present comparisons of performance of the proposed method with existing approaches in simulation studies, and in analysis of a dataset collected during a luminance exposure experiment.