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In recent years, incomplete multi-view clustering (IMVC), which studies the challenging multi-view clustering problem on missing views, has received growing research interests. Previous IMVC methods suffer from the following issues: (1) the inaccurate imputation for missing data, which leads to suboptimal clustering performance, and (2) most existing IMVC models merely consider the explicit presence of graph structure in data, ignoring the fact that latent graphs of different views also provide valuable information for the clustering task. To overcome such challenges, we present a novel method, termed Adaptive feature imputation with latent graph for incomplete multi-view clustering (AGDIMC). Specifically, it captures the embbedded features of each view by incorporating the view-specific deep encoders. Then, we construct partial latent graphs on complete data, which can consolidate the intrinsic relationships within each view while preserving the topological information. With the aim of estimating the missing sample based on the available information, we utilize an adaptive imputation layer to impute the embedded feature of missing data by using cross-view soft cluster assignments and global cluster centroids. As the imputation progresses, the portion of complete data increases, contributing to enhancing the discriminative information contained in global pseudo-labels. Meanwhile, to alleviate the negative impact caused by inferior impute samples and the discrepancy of cluster structures, we further design an adaptive imputation strategy based on the global pseudo-label and the local cluster assignment. Experimental results on multiple real-world datasets demonstrate the effectiveness of our method over existing approaches.