Graph theory analysis, as a mathematical tool, has been widely employed in studying the connectivity of the brain to explore the structural organization. Through the computation of graph theory metrics, it can effectively reveal the nonlinear and complex behavioral features of neuroimaging data, e.g., Electroencephalogram (EEG) and Magnetic Resonance Imaging (MRI), which are often challenging to interpret using simple linear methods. Graph neural networks (GNNs), employing deep learning, offer a more flexible approach to handling large-scale, high-dimensional brain network data. This review aims to investigate the applications of graph theory and Graph Neural Networks in the diagnosis of neurological disorders. The complexity and multi-level features of neurological disorders pose challenges for traditional methods in addressing such issues. The paper begins by introducing the fundamental principles of graph theory and GNNs, elucidates the mechanisms behind diagnosis process using these methods, and then provides a comprehensive overview of their specific applications. Finally, it discusses and summarizes the current challenges in this research field, proposing future directions for development. In conclusion, this review provides a thorough theoretical foundation and methodological insight for exploring the potential applications of graph theory and GNNs in the diagnosis of neurological disorders.