π-index
The π-index (Vinkler 2009) is similar to other measures of the quality of the h-index core, except that it uses its own unique definition of the core. For this index, the core publication set Pπ is defined as the square-root of the total number of publications, truncated down to the nearest integer (e.g., for 80 publications, the square-root of 80 is 8.944, so Pπ would equal 8):
$$P_\pi=\text{floor}\left({\sqrt{P}}\right).$$The π-index is 1/100th of the total citations within this core:
$$\pi=\frac{C^\pi}{100}=\frac{\sum\limits_{i=1}^{P_\pi}{C_i}}{100}.$$Example
Publications are ordered by number of citations, from highest to lowest.
Citations (Ci) | 59 | 26 | 16 | 11 | 11 | 10 | 4 | 3 | 3 | 2 | 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 |
Pπ = 4 |
The π-core is the floor of the square-root of the total number of publications, thus Pπ = floor(√18) = floor(4.24) = 4. The π-index is 1/100th of the sum of the citations within the π-core, thus π = 112/100 = 1.12.
History
Year | π |
---|---|
1997 | 0.0200 |
1998 | 0.1000 |
1999 | 0.3700 |
2000 | 0.6000 |
2001 | 1.1200 |
2002 | 1.7200 |
2003 | 2.7200 |
2004 | 3.8100 |
2005 | 5.5300 |
2006 | 8.5500 |
2007 | 11.1700 |
2008 | 13.4900 |
2009 | 15.9100 |
2010 | 20.4100 |
2011 | 23.1300 |
2012 | 26.4000 |
2013 | 29.3700 |
2014 | 35.6500 |
2015 | 39.3500 |
2016 | 43.4700 |
2017 | 47.1600 |
2018 | 50.8400 |
2019 | 54.3800 |
2020 | 57.9900 |
2021 | 61.4500 |
2022 | 69.8600 |
2023 | 73.5500 |
2024 | 77.3700 |
2025 | 79.1600 |
References
- Vinkler, P. (2009) The p-index: A new indicator for assessing scientific impact. Journal of Information Science 35(5):602–612.