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The gene regulatory structure of cells involves not only the regulatory relationship between two genes, but also the cooperative associations of multiple genes. However, most gene regulatory network inference methods for single cell only focus on and infer the regulatory relationships of pairs of genes, ignoring the global regulatory structure which is crucial to identify the regulations in the complex biological systems. Here, we proposed a graph-based Deep learning model for Regulatory networks Inference among Genes (DeepRIG) from single-cell RNA-seq data. To learn the global regulatory structure, DeepRIG builds a prior regulatory graph by transforming the gene expression of data into the co-expression mode. Then it utilizes a graph autoencoder model to embed the global regulatory information contained in the graph into gene latent embeddings and to reconstruct the gene regulatory network. Extensive benchmarking results demonstrate that DeepRIG can accurately reconstruct the gene regulatory networks and outperform existing methods on multiple simulated networks and real-cell regulatory networks. Additionally, we applied DeepRIG to the samples of human peripheral blood mononuclear cells and triple-negative breast cancer, and presented that DeepRIG can provide accurate cell-type-specific gene regulatory networks inference and identify novel regulators of progression and inhibition. Author summary: Although many methods have been proposed to infer the gene regulatory network of a single cell, they only focus on the regulatory relationships of pairs of genes and ignore the global regulatory structure. Here, we present a deep learning-based model to learn the global regulatory structure and reconstruct the gene regulatory networks from single-cell RNA sequencing data with a graph view. We utilize the weighted gene co-expression analysis to build a prior regulatory graph of gene and a graph autoencoder to deconstruct the latent regulatory structure among genes. We performed extensive experiments on varieties of single-cell RNA sequencing datasets and compared our method with 9 stat-of-the-art gene regulatory network inference method. The results show that our method can significantly improve the accuracy of gene regulatory network inference and can be applied to identify key regulators in a wide range of scenarios. [ABSTRACT FROM AUTHOR]