The excessive consumption of marijuana can induce substantial psychological and social consequences. In this investigation, we propose an elucidative framework termed high-order graph attention neural networks (HOGANN) for the classification of Marijuana addiction, coupled with an analysis of localized brain network communities exhibiting abnormal activities among chronic marijuana users. HOGANN integrates dynamic intrinsic functional brain networks, estimated from functional magnetic resonance imaging (fMRI), using graph attention-based long short-term memory (GAT-LSTM) to capture temporal network dynamics. We employ a high-order attention module for information fusion and message passing among neighboring nodes, enhancing the network community analysis. Our model is validated across two distinct data cohorts, yielding substantially higher classification accuracy than benchmark algorithms. Furthermore, we discern the most pertinent subnetworks and cognitive regions affected by persistent marijuana consumption, indicating adverse effects on functional brain networks, particularly within the dorsal attention and frontoparietal networks. Intriguingly, our model demonstrates superior performance in cohorts exhibiting prolonged dependence, implying that prolonged marijuana usage induces more pronounced alterations in brain networks. The model proficiently identifies craving brain maps, thereby delineating critical brain regions for analysis.