In recent years, graph-based models and ranking algorithms have drawn considerable attention from the extractive document summarization community. Most existing approaches take into account sentence-level relations (e.g. sentence similarity) but neglect the difference among documents and the influence of documents on sentences. In this paper, we present a novel document-sensitive graph model that emphasizes the influence of global document set information on local sentence evaluation. By exploiting document–document and document–sentence relations, we distinguish intra-document sentence relations from inter-document sentence relations. In such a way, we move towards the goal of truly summarizing multiple documents rather than a single combined document. Based on this model, we develop an iterative sentence ranking algorithm, namely DsR (Document-Sensitive Ranking). Automatic ROUGE evaluations on the DUC data sets show that DsR outperforms previous graph-based models in both generic and query-oriented summarization tasks.