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 | 8.6667 |
| 1999 | 25.8413 |
| 2000 | 45.5357 |
| 2001 | 72.9037 |
| 2002 | 72.3182 |
| 2003 | 92.0769 |
| 2004 | 149.6733 |
| 2005 | 248.6646 |
| 2006 | 335.2665 |
| 2007 | 516.2148 |
| 2008 | 737.9912 |
| 2009 | 1109.9441 |
| 2010 | 974.0819 |
| 2011 | 1267.5620 |
| 2012 | 2339.2865 |
| 2013 | 2591.7486 |
| 2014 | 3180.7728 |
| 2015 | 3235.8121 |
| 2016 | 3175.6132 |
| 2017 | 4029.5548 |
| 2018 | 3577.0132 |
| 2019 | 3396.7762 |
| 2020 | 3369.8698 |
| 2021 | 3320.1706 |
| 2022 | 3763.1485 |
| 2023 | 3695.7744 |
| 2024 | 3751.6005 |
| 2025 | 3993.4161 |
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.