Objective: To reveal the correlation characteristics of h-index family, and make empirical study on the research influence of 37 university libraries in Shandong province, and provide basis for librarians and relevant institutions when they make decisions about interlibrary research evaluation, communication and training. Methods: Using Chinese Citations Database as data source, the paper made statistical analysis and the total number of papers and the times cited with h-index family in statistical period from 1996 to 2010. Results: The results indicate that library of Ludong University Library had a significant value and some university libraries perform well on h-index family such as Yantai University Library. Library of Taishan Medical University is expected to improve research influence significantly with a considerable number of potentially highly cited papers. The results also show that there is a power-law relation between h-index and sum of the times cited, the same as the total number of papers, and there is a linear relationship between any two. Conclusion: The increment of the total times cited and the total number of papers will contribute as extensive descending phenomenon to that of h-index family. Libraries should pay more attention to those potentially highly cited papers which will contribute to its g-index in order to enhance h-index and S-index to achieve the desire of improving research influence.%为了揭示“h指数族”各项指数的相关性特点,对山东省内37所本科高校图书馆科研影响力进行综合实证研究,为图书馆工作者及相关机构进行馆际科研评价、交流和培训等提供决策依据.文章以《中国引文数据库》为数据源,用“h指数族”各项指数对评价机构在1996-2010年的论文数量和总被引频次进行统计分析.结论如下:鲁东大学图书馆h指数族取值特性异常显著；烟台大学图书馆等h指数族排名位次靠前；泰山医学院图书馆具备相当数量的潜在高被引论文,预期其科研影响力将会有显著提升.h指数族与论文数量和被引频次之间呈幂律关系,h指数族两两之间呈线性关系.图书馆h指数族取值随着图书馆论文数量和总被引频次的增长存在“规模效益递减”现象；图书馆应该密切关注能提升其g指数的潜在高被引论文,从而实现提升h指数和S指数、不断提高科研影响力的愿望.
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