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 | 3.1500 |
1999 | 25.8413 |
2000 | 66.8571 |
2001 | 77.1282 |
2002 | 72.2416 |
2003 | 116.5109 |
2004 | 151.9073 |
2005 | 249.1251 |
2006 | 383.7143 |
2007 | 516.8177 |
2008 | 730.9163 |
2009 | 1336.3646 |
2010 | 1126.7631 |
2011 | 1448.6647 |
2012 | 2382.8788 |
2013 | 2645.7893 |
2014 | 3209.2657 |
2015 | 3246.5952 |
2016 | 3185.7698 |
2017 | 4033.1959 |
2018 | 3510.8026 |
2019 | 3366.0296 |
2020 | 3336.4646 |
2021 | 3567.2627 |
2022 | 3694.5591 |
2023 | 3895.9192 |
2024 | 3832.7114 |
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.