We propose a two-dimensional bibliometric index that strikes a balance between quantity (as measured by the number of publications of a researcher) and quality (as measured by the number of citations to those publications). While the square of h -index is determined by the maximum area square that fits under the citation curve of an author when plotting the number of citations in decreasing order, the rec -index is determined by the maximum area rectangle that fits under the curve. In this context we may distinguish between authors with a few very highly-cited publications, who may have carried out some influential research, and prolific authors, who may have many publications but fewer citations per publication. The influence of a researcher may be measured via a restricted version of the rec -index, the $${rec}_{I}$$ rec I -index, which is the maximum area vertical rectangle that fits under the citation curve. Similarly, the prolificity of a researcher may be measured via the $${rec}_{P}$$ rec P -index, which is the maximum area horizontal rectangle that fits under the citation curve. This leads to the proposal of the two-dimensional bibliometric index $$({rec}_{I}, {rec}_{P})$$ ( rec I , rec P ) , which captures both aspects of a researcher’s output. We present a comprehensive empirical analysis of this two-dimensional index on two datasets: a large set of Google Scholar profiles (representing “typical” researchers) and a small set of Nobel prize winners. Our results demonstrate the potential of this two-dimensional index, since for both data sets there is a statistically significant number of researchers for whom $${rec}_{I}$$ rec I is greater than $${rec}_{P}$$ rec P . In particular, for nearly 25% of the Google Scholar researchers and for nearly 60% of the Nobel prize winners, $${rec}_{I}$$ rec I is greater than $${rec}_{P}$$ rec P .

中文翻译：

---

反映质量和数量的二维文献计量索引

我们提出了一个二维文献计量索引，它在数量（以研究人员的出版物数量衡量）和质量（以这些出版物的引用次数衡量）之间取得平衡。虽然 h-index 的平方由在以降序绘制引用次数时适合作者的引用曲线下的最大面积平方决定，但 rec-index 由适合曲线下的最大面积矩形决定。在这种情况下，我们可以区分拥有少数高引用出版物的作者，他们可能进行了一些有影响力的研究，以及多产的作者，他们可能有很多出版物但每次出版物的引用较少。研究人员的影响力可以通过 rec -index 的受限版本来衡量，$${rec}_{I}$$ rec I -index，这是适合引用曲线的最大面积垂直矩形。类似地，研究人员的多产可以通过 $${rec}_{P}$$ rec P 指数来衡量，它是适合引用曲线的最大面积水平矩形。这导致了二维文献计量索引 $$({rec}_{I}, {rec}_{P})$$ ( rec I , rec P ) 的提议，它捕获了研究人员输出的两个方面。我们在两个数据集上对这个二维索引进行了全面的实证分析：一组大型 Google Scholar 个人资料（代表“典型”研究人员）和一小部分诺贝尔奖获得者。我们的结果证明了这种二维指数的潜力，因为对于这两个数据集，有大量研究人员认为 $${rec}_{I}$$ rec I 大于 $${rec}_{ P}$$ rec P 。