Graphical models are a ubiquitous tool for identifying dependencies among components of high-dimensional multivariate data. Recently, these tools have been extended to estimate dependencies between components of multivariate functional data by applying multivariate methods to the coefficients of truncated basis expansions. A key difficulty compared to multivariate data is that the covariance operator is compact, and thus not invertible.  In this talk, we will discuss a property called partial separability that circumvents the invertibility issue and identifies the functional graphical model with a countable collection of finite-dimensional graphical models.  This representation allows for the development of simple and intuitive estimators. Finally, we will demonstrate the empirical findings of our method through simulation and analysis of functional brain connectivity during a motor task.