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Graph neural networks (GNNs) have been successfully applied to early mild cognitive impairment (EMCI) detection, with the usage of elaborately designed features constructed from blood oxygen level-dependent (BOLD) time series. However, few works explored the feasibility of using BOLD signals directly as features. Meanwhile, existing GNN-based methods primarily rely on hand-crafted explicit brain topology as the adjacency matrix, which is not optimal and ignores the implicit topological organization of the brain. In this paper, we propose a spatial temporal graph convolutional network with a novel graph structure self-learning mechanism for EMCI detection. The proposed spatial temporal graph convolution block directly exploits BOLD time series as input features, which provides an interesting view for rsfMRI-based preclinical AD diagnosis. Moreover, our model can adaptively learn the optimal topological structure and refine edge weights with the graph structure self-learning mechanism. Results on the Alzheimer's Disease Neuroimaging Initiative (ADNI) database show that our method outperforms state-of-the-art approaches. Biomarkers consistent with previous studies can be extracted from the model, proving the reliable interpretability of our method.