two-sided h-index
The two-sided h-index (García-Pérez 2012) is an extension of the multidimensional h-index, which recalcultes h not only for the tail of the distribution (as in the multidimensional version) but also for the excess citations from h-core publications beyond those necessary to reach h, thus providing a multidimensional measure of both the upper and tail parts of the citation distribution.
The tail half of the two-sided h-index is identical to the multidimensional h-index (although, notationally, the original h is now designated h0). To calculate the upper part, after the initial h is determined, one calculates h-1 (the value immediately in front of h) by first subtracting h from the citation count for all of the publications in the core, then determining a new h from this reduced citation set.
Graphically, this is finding the largest square which can fit on top of the original square representing h. This process is repeated for the remaining excess citations in the (new) core.
To ensure symmetry, we calculate h±k such that the number of steps above the core is identical to the number of steps in the tail.
Example
Publications are ordered by number of citations, from highest to lowest. Publications within the original core have h citations removed at each step; publications in the original tail are ranked independently at each subsequent step.
| Citations (Ci) | 47 | 26 | 19 | 15 | 11 | 10 | 4 | 3 | 2 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Rank (i) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 |
| h0 = 6 | ||||||||||||||||||
| Adjusted Citations (Ci) | 41 | 20 | 13 | 9 | 5 | 4 | 4 | 3 | 2 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 |
| Rank (i) | 1 | 2 | 3 | 4 | 5 | 6 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| h-1 = 5 | h1 = 2 | |||||||||||||||||
| Adjusted Citations (Ci) | 36 | 15 | 8 | 4 | 0 | 2 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | |||
| Rank (i) | 1 | 2 | 3 | 4 | 5 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |||
| h-2 = 4 | h2 = 1 | |||||||||||||||||
| Adjusted Citations (Ci) | 32 | 11 | 4 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | |||||
| Rank (i) | 1 | 2 | 3 | 4 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | |||||
| h-3 = 3 | h3 = 1 | |||||||||||||||||
| Adjusted Citations (Ci) | 29 | 8 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | |||||||
| Rank (i) | 1 | 2 | 3 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | |||||||
| h-4 = 2 | h4 = 1 | |||||||||||||||||
| Adjusted Citations (Ci) | 27 | 6 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | |||||||||
| Rank (i) | 1 | 2 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | |||||||||
| h-5 = 2 | h5 = 1 | |||||||||||||||||
| Adjusted Citations (Ci) | 25 | 4 | 1 | 0 | 0 | 0 | 0 | 0 | ||||||||||
| Rank (i) | 1 | 2 | 1 | 2 | 3 | 4 | 5 | 6 | ||||||||||
| h-6 = 2 | h6 = 1 |
History
| Year | h±k |
|---|---|
| 1997 | [0, 1, 1] |
| 1998 | [1, 1, 2, 2, 1] |
| 1999 | [2, 2, 2, 3, 2, 1, 1] |
| 2000 | [3, 5, 2] |
| 2001 | [2, 2, 2, 3, 4, 5, 6, 2, 1, 1, 1, 1, 1] |
| 2002 | [3, 3, 4, 5, 5, 8, 4, 3, 1, 1, 1] |
| 2003 | [4, 4, 5, 6, 11, 5, 3, 1, 1] |
| 2004 | [6, 7, 8, 9, 12, 7, 3, 1, 1] |
| 2005 | [6, 6, 7, 8, 9, 10, 15, 6, 3, 2, 1, 1, 1] |
| 2006 | [8, 9, 11, 17, 7, 4, 3] |
| 2007 | [9, 10, 13, 19, 8, 3, 2] |
| 2008 | [11, 11, 16, 21, 10, 2, 2] |
| 2009 | [9, 10, 12, 14, 17, 25, 6, 3, 1, 1, 1] |
| 2010 | [9, 11, 11, 14, 15, 17, 26, 9, 5, 1, 1, 1, 1] |
| 2011 | [12, 13, 15, 16, 18, 29, 9, 4, 2, 1, 1] |
| 2012 | [11, 12, 13, 15, 17, 21, 32, 7, 4, 2, 2, 1, 1] |
| 2013 | [11, 11, 13, 15, 17, 19, 23, 33, 7, 5, 2, 1, 1, 1, 1] |
| 2014 | [11, 11, 12, 13, 14, 17, 18, 19, 24, 34, 8, 5, 3, 2, 1, 1, 1, 1, 1] |
| 2015 | [13, 15, 16, 17, 19, 19, 24, 35, 9, 5, 3, 2, 2, 2, 1] |
| 2016 | [14, 15, 16, 16, 18, 19, 20, 24, 35, 10, 6, 3, 2, 2, 1, 1, 1] |
| 2017 | [16, 16, 17, 18, 19, 20, 25, 37, 11, 5, 3, 2, 2, 1, 1] |
| 2018 | [16, 16, 17, 19, 19, 21, 27, 37, 12, 5, 4, 2, 2, 1, 1] |
| 2019 | [15, 16, 16, 18, 19, 19, 23, 28, 37, 13, 6, 4, 2, 2, 1, 1, 1] |
| 2020 | [16, 18, 19, 19, 24, 29, 38, 12, 6, 5, 3, 2, 2] |
| 2021 | [18, 18, 19, 22, 24, 29, 40, 13, 6, 5, 2, 2, 2] |
| 2022 | [17, 18, 18, 21, 22, 24, 30, 41, 13, 6, 5, 3, 2, 2, 1] |
| 2023 | [18, 19, 21, 22, 25, 30, 42, 14, 6, 5, 3, 2, 2] |
| 2024 | [18, 20, 21, 22, 25, 30, 42, 15, 6, 5, 3, 2, 1] |
References
- García-Pérez, M.A. (2012) An extension of the h index that covers the tail and the top of the citation curve and allows ranking researchers with similar h. Journal of Informetrics 6:689–699.