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Extractive document summarization (EDS) is usually seen as a sequence labeling task, which extracts sentences from a document one by one to form a summary. However, extracting sentences separately ignores the relationship between the sentences and documents. One solution is to use sentence position information to enhance sentence representation, but this will cause the sentence-leading bias problem, especially in news datasets. In this paper, we propose a novel sentence centrality for the EDS task to address these two problems. The sentence centrality is based on directed graphs, while reflecting the sentence-document relationship, it also reflects the sentence position information in the document. We implicitly strengthen the relevance of sentences and documents by using sentence centrality to enhance sentence representation. Notably, we replaced the sentence position information with sentence centrality to reduce sentence-leading bias without causing model performance degradation. Experiments on the CNN/Daily Mail dataset showed that EDS models with sentence centrality significantly improved compared with baseline models. [ABSTRACT FROM AUTHOR]