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• We design a MCI-graph framework which integrates both non-image information and image information. We use LWCC to extract the feature to avoid the high dimensional features. • We devise various parallel GCN layers using multiple inputs from the random walk embedding theory, which is able to identify the essential MCI information from the GCN graph embedding. • The random walk embeddings on the graph can explore the high order similarity of features. • We fuse the information from the functional networks and structural networks using a MSE-GCN model to improve prediction performance. As an early stage of Alzheimer's disease (AD), mild cognitive impairment (MCI) is able to be detected by analyzing the brain connectivity networks. For this reason, we devise a new framework via multi-scale enhanced graph convolutional network (MSE-GCN) for MCI detection, which integrates the structural and functional information from the diffusion tensor imaging (DTI) and resting-state functional magnetic resonance imaging (R-fMRI), respectively. Specifically, both information in the brain connective networks is first integrated based on the local weighted clustering coefficients (LWCC), which is concatenated as the feature vector for representing a population graph's vertice. Simultaneously, the gender and age information in each subject are integrated with the structural and functional features to construct a sparse graph. Then, various parallel graph convolutional network (GCN) layers with multiple inputs are designed from the embedding from random walk embeddings in the GCN to identify the essential MCI graph information. Finally, all GCN layers' outputs are concatenated via the fully connection layer to perform disease detection. The experimental results on the public Alzheimer's Disease Neuroimaging Initiative (ADNI) database show that our method is promising to detect MCI and superior to other competing algorithms, with a mean classification accuracy of 90.39% in the detection tasks. [ABSTRACT FROM AUTHOR]