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 | 96.5035 |
| 2004 | 156.1938 |
| 2005 | 216.3783 |
| 2006 | 339.0852 |
| 2007 | 523.7401 |
| 2008 | 740.0321 |
| 2009 | 1122.3787 |
| 2010 | 1006.2250 |
| 2011 | 1277.4840 |
| 2012 | 2384.1111 |
| 2013 | 2647.1323 |
| 2014 | 3220.7935 |
| 2015 | 3258.0004 |
| 2016 | 3193.3753 |
| 2017 | 4070.5063 |
| 2018 | 3539.8222 |
| 2019 | 3403.9384 |
| 2020 | 3362.3901 |
| 2021 | 3296.2900 |
| 2022 | 3729.2269 |
| 2023 | 3961.4760 |
| 2024 | 3520.8151 |
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.