This work proposes a methodology to analyze (in)dependencies in compositional data using graphical models. By transforming compositional data into an unconstrained space, we apply Gaussian graphical models to identify meaningful dependency structures. Our approach relies on estimating block-diagonal covariance matrices, ensuring compatibility with compositional constraints. The optimal structure is selected via a penalized likelihood criterion and cross-validation. To illustrate its effectiveness, we apply the proposed method to energy consumption data from 31 countries, uncovering key dependencies among energy sources and providing insights into their interconnections.