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Due to the explosion of knowledge in the library, the librarians need to make effective decisions in book acquisition under the limited budget. Since librarians can not fully realize the needs of readers, many libraries provide the book recommendation service such that the readers can recommend the books to the libraries. However, the readers may only recommend the books in accordance with their own interest, resulting in the recommended books not meeting the needs of other readers. To facilitate decision-making in book acquisition, this paper used the social network to establish the relationships between the recommender and his/her related readers via the historical circulation records. Upon the social network, this paper uses social computing to evaluate the representative degree of the recommender, and then rank the recommended books. The retrospective and empirical studies are performed to show the effectiveness of the proposed ranking system by the spearman's rank correlation coefficient. That is, the ranking of the recommended books by the proposed system is very like the two rankings of these books from the analysis of the historical circulation records and the librarian.