The SUDMEX CONN dataset, comprising extensive brain imaging data and demographic information, serves as a valuable resource for exploring the neurobiological mechanisms underlying Cocaine Use Disorder (CUD). In this study, we employed Graph Convolutional Networks (GCNs) to diagnose CUD using resting-state functional magnetic resonance imaging (rs-fMRI) data. Kernel Principal Component Analysis (PCA) was utilized for dimensionality reduction and enhancing computational efficiency. We construct brain graphs from the augmented rs-fMRI images and use GCN for the classification task. The simulation results demonstrate that the GCN model, trained on the SUDMEX CONN dataset, can accurately distinguish between CUD patients and healthy controls (HC) based on brain connectivity patterns. Our approach provides valuable insights into the underlying neurobiological mechanisms of CUD and highlights the potential of innovative tools for understanding and treating this chronic disorder. Ablation studies confirmed kernel PCA is highly efficient in reducing the dataset dimensionality and accelerating the simulation time. The simulation results revealed that the combined approach of GCN and kernel PCA could achieve an impressive accuracy of 98.25 % in diagnosing CUD cases. Our implementation codes are available at https://github.com/MehdiMatinfar/GPCA.