Graphical models are frequently used to explore networks among a set of variables. In the first part of this talk, we explore the practical performance of several sparse graphical methods and several selection criteria for estimating brain networks using both simulated multivariate normal data and autocorrelated data. We use evaluation criteria to compare the methods and thoroughly discuss the superiority and deficiency of each of them. We also apply the methods to a resting state functional magnetic resonance imaging (fMRI) experiment and to a language processing experiment. In the second part of the talk, we consider data-driven methods that detect change points in the network structure of a multivariate time series taken from brain imaging experiments. The methods allow for estimation of both the time of change in the network structure and the graph between each pair of change points, without prior knowledge of the number or location of the change points. The methods are applied to various simulated high dimensional data sets as well as to fMRI data sets. The results illustrate the methods’ ability to observe how the network structure between different brain regions changes over the experimental time course.