In the present research, the effectiveness of large-scale Augmented Granger Causality (lsAGC) as a tool for gauging brain network connectivity was examined to differentiate between marijuana users and typical controls by utilizing resting-state functional Magnetic Resonance Imaging (fMRI). The relationship between marijuana consumption and alterations in brain network connectivity is a recognized fact in scientific literature. This study probes how lsAGC can accurately discern these changes. The technique used integrates dimension reduction with the augmentation of source time-series in a model that predicts time-series, which helps in estimating the directed causal relationships among fMRI time-series. As a multivariate approach, lsAGC uncovers the connection of the inherent dynamic system while considering all other time-series. A dataset of 60 adults with an ADHD diagnosis during childhood, drawn from the Addiction Connectome Preprocessed Initiative (ACPI), was used in the study. The brain connections assessed by lsAGC were utilized as classification attributes. A Graph Attention Neural Network (GAT) was chosen to carry out the classification task, particularly for its ability to harness graph-based data and recognize intricate interactions between brain regions, making it appropriate for fMRI-based brain connectivity data. The performance was analyzed using a five-fold cross-validation system. The average accuracy achieved by the correlation coefficient method was roughly 52.98%, with a 1.65 standard deviation, whereas the lsAGC approach yielded an average accuracy of 61.47%, with a standard deviation of 1.44. The suggested method enhances the body of knowledge in the field of neuroimaging-based classification and emphasizes the necessity to consider directed causal connections in brain network connectivity analysis when studying marijuana's effects on the brain.