k-index
The k-index (Ye and Rousseau 2010) is a measure of the relative impact of citations within the h-index core to those in the tail. Specifically, it is the ratio of impact over the tail-core ratio and is calculated as
$$k=\frac{C^PC^h}{P\left(C^P-C^h\right)}.$$This metric is specifically meant to be used in a time-series analysis where k is calculated for multiple time points.History
| Year | k |
|---|---|
| 1997 | 0.3333 |
| 1998 | 7.5000 |
| 1999 | 25.8413 |
| 2000 | 44.4000 |
| 2001 | 81.7949 |
| 2002 | 62.8364 |
| 2003 | 95.9832 |
| 2004 | 155.0004 |
| 2005 | 253.9498 |
| 2006 | 342.2667 |
| 2007 | 524.3494 |
| 2008 | 742.0757 |
| 2009 | 1124.8956 |
| 2010 | 1006.2250 |
| 2011 | 1272.7129 |
| 2012 | 2387.1695 |
| 2013 | 2650.0556 |
| 2014 | 3222.8917 |
| 2015 | 3257.0492 |
| 2016 | 3196.7584 |
| 2017 | 4076.4532 |
| 2018 | 3578.1038 |
| 2019 | 3395.9929 |
| 2020 | 3355.6092 |
| 2021 | 3278.5064 |
| 2022 | 3708.1059 |
| 2023 | 4025.2825 |
| 2024 | 3770.7950 |
| 2025 | 3745.7255 |
References
- Ye, F.Y., and R. Rousseau (2010) Probing the h-core: An investigation of the tail-core ratio for rank distributions. Scientometrics 84(2):431–439.