  Graph Neural Networks (GNNs) have received considerable attention since its
introduction. It has been widely applied in various fields due to its ability
to represent graph structured data. However, the application of GNNs is
constrained by two main issues. Firstly, the "over-smoothing" problem restricts
the use of deeper network structures. Secondly, GNNs' applicability is greatly
limited when nodes and edges are not clearly defined and expressed, as is the
case with EEG data.In this study, we proposed an innovative approach that
harnesses the distinctive properties of the graph structure's Markov Chain to
optimize the sampling depth of deep graph convolution networks. We introduced a
tailored method for constructing graph structures specifically designed for
analyzing EEG data, alongside the development of a vertex-level GNN
classification model for precise detection of mental disorders. In order to
verify the method's performance, we conduct experiments on two disease datasets
using a subject-independent experiment scenario. For the Schizophrenia (SZ)
data, our method achieves an average accuracy of 100% using only the first 300
seconds of data from each subject. Similarly, for Major Depressive Disorder
(MDD) data, the method yields average accuracies of over 99%. These experiments
demonstrate the method's ability to effectively distinguish between healthy
control (HC) subjects and patients with mental disorders. We believe this
method shows great promise for clinical diagnosis.
