In this study, we propose a new index for measuring excellence in science which is based on collaborations (co-authorship distances) in science. The index is based on the Erd\H{o}s number - a number that was introduced several years ago. We propose to focus with the new index on laureates of prestigious prizes in a certain field and to measure co-authorship distances between the laureates and other scientists. To exemplify and explain our proposal, we computed the proposed index in the field of quantitative science studies (PWIPM). The Derek de Solla Price Memorial Award (Price Medal, PM) is awarded to outstanding scientists in the field. We tested the convergent validity of the PWIPM. We were interested whether the indicator is related to an established bibliometric indicator: P(top 10%). The results show that the coefficients for the correlation between PWIPM and P(top 10%) are high (in cases when a sufficient number of papers have been considered for a reliable assessment of performance). Therefore, measured by an established indicator for research excellence, the new PWI indicator seems to be convergently valid and, therefore, might be a possible alternative for established (bibliometric) indicators - with a focus on prizes.

翻译：在本研究中，我们提出了一种基于科学合作（合著距离）来衡量科学卓越性的新指数。该指数基于Erdős数——一个多年前引入的概念。我们建议将新指数聚焦于特定领域内权威奖项的获奖者，并衡量获奖者与其他科学家之间的合著距离。为举例说明并阐释我们的提议，我们计算了定量科学研究领域中的提议指数（PWIPM）。Derek de Solla Price纪念奖（Price Medal, PM）授予该领域的杰出科学家。我们检验了PWIPM的收敛效度，关注该指标是否与已建立的文献计量指标P(top 10%)相关。结果表明，PWIPM与P(top 10%)之间的相关系数较高（在论文数量足以可靠评估绩效的情况下）。因此，通过衡量研究卓越性的成熟指标进行验证，新PWI指数似乎具有收敛效度，并可能成为现有（文献计量）指标的一种可行替代方案——其核心聚焦于奖项。