normalized hi-index
Similar to the adapted pure h-index (fractional credit), the normalized hi-index (Wohlin 2009) is designed to adjust the h-index for multiple authors by adjusting the citation count by the number of authors. The primary difference is the new citation value is calculated by dividing by the number of authors (Ci / Ai) rather than the square-root of the number of authors. Publications are again ranked by these new citation per author values and the normalized hi-index is calculated in the same manner as the h-index, that is an author has a normalized hi-index of hi-norm when hi-norm of their publications have at least hi-norm citations per author, or
$$h_{i\text{-norm}}=\underset{i}{\max}\left(i \leq \frac{C_i}{A_i}\right).$$This is identical to what Egghe (2008) called the fractional citation h-index (hf) and was again re-invented by Abbas (2011) as the equally-weighted h-index (he).
Example
Publications are ordered by adjusted number of citations, from highest to lowest.
| Citations (Ci) | 57 | 11 | 26 | 16 | 12 | 10 | 2 | 4 | 1 | 1 | 3 | 1 | 1 | 0 | 0 | 0 | 0 | 0 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Authors (Ai) | 3 | 1 | 3 | 2 | 3 | 4 | 1 | 4 | 1 | 1 | 4 | 2 | 4 | 4 | 2 | 1 | 1 | 1 |
| Adjusted Citations (Ci/Ai) | 19.00 | 11.00 | 8.67 | 8.00 | 4.00 | 2.50 | 2.00 | 1.00 | 1.00 | 1.00 | 0.75 | 0.50 | 0.25 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| Rank (i) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 |
| hi-norm = 4 |
The largest rank where i ≤ Ci/Ai is 4.
History
| Year | hi-norm |
|---|---|
| 1997 | 0 |
| 1998 | 1 |
| 1999 | 2 |
| 2000 | 4 |
| 2001 | 4 |
| 2002 | 6 |
| 2003 | 8 |
| 2004 | 9 |
| 2005 | 12 |
| 2006 | 14 |
| 2007 | 16 |
| 2008 | 19 |
| 2009 | 20 |
| 2010 | 21 |
| 2011 | 23 |
| 2012 | 24 |
| 2013 | 26 |
| 2014 | 26 |
| 2015 | 26 |
| 2016 | 27 |
| 2017 | 27 |
| 2018 | 27 |
| 2019 | 28 |
| 2020 | 29 |
| 2021 | 31 |
| 2022 | 33 |
| 2023 | 33 |
| 2024 | 33 |
References
- Abbas, A.M. (2011) Weighted indices for evaluating the quality of research with multiple authorship. Scientometrics 88:107–131.
- Egghe, L. (2008) Mathematical theory of the h- and g-index in case of fractional counting of authorship. Journal of the American Society for Information Science and Technology 59(10):1608–1616.
- Wohlin, C. (2009) A new index for the citation curve of researchers. Scientometrics 81(2):521–533.