Functional magnetic resonance imaging (fMRI) provides insights into complex patterns of brain functional changes, making it a valuable tool for exploring addiction-related brain connectivity. However, effectively extracting addiction-related brain connectivity from fMRI data remains challenging due to the intricate and non-linear nature of brain connections. Therefore, this paper proposed the Graph Diffusion Reconstruction Network (GDRN), a novel framework designed to capture addiction-related brain connectivity from fMRI data acquired from addicted rats. The proposed GDRN incorporates a diffusion reconstruction module that effectively maintains the unity of data distribution by reconstructing the training samples, thereby enhancing the model's ability to reconstruct nicotine addiction-related brain networks. Experimental evaluations conducted on a nicotine addiction rat dataset demonstrate that the proposed GDRN effectively explores nicotine addiction-related brain connectivity. The findings suggest that the GDRN holds promise for uncovering and understanding the complex neural mechanisms underlying addiction using fMRI data.