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This study investigates the problem of multi-view subspace clustering, the goal of which is to explore the underlying grouping structure of data collected from different fields or measurements. Since data do not always comply with the linear subspace models in many real-world applications, most existing multi-view subspace clustering methods that based on the shallow linear subspace models may fail in practice. Furthermore, underlying graph information of multi-view data is always ignored in most existing multi-view subspace clustering methods. To address aforementioned limitations, we proposed the novel multi-view subspace clustering networks with local and global graph information, termed MSCNLG, in this paper. Specifically, autoencoder networks are employed on multiple views to achieve latent smooth representations that are suitable for the linear assumption. Simultaneously, by integrating fused multi-view graph information into self-expressive layers, the proposed MSCNLG obtains the common shared multi-view subspace representation, which can be used to get clustering results by employing the standard spectral clustering algorithm. As an end-to-end trainable framework, the proposed method fully investigates the valuable information of multiple views. Comprehensive experiments on six benchmark datasets validate the effectiveness and superiority of the proposed MSCNLG.