# Michael S. Rosenberg’s Laboratory

Computational Evolutionary Biology & Bioinformatics

E-mail: msr@asu.edu
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## π-index

The π-index (Vinkler 2009) is similar to other measures of the quality of the Hirsch 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) Rank (i) 42 36 14 11 9 9 3 2 2 2 1 1 1 0 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Pπ = 4

The π-core is the floor of the square-root of the total number of publications, thus Pπ = floor(√16) = floor(4.00) = 4. The π-index is 1/100th of the sum of the citations within the π-core, thus π = 103/100 = 1.03.

Yearπ
19970.0200
19980.0900
19990.2700
20000.4500
20011.0300
20021.7200
20032.5600
20043.8900
20055.3600
20067.1400
20079.9700
200812.2000
200914.6400
201017.2200
201120.6300
201222.0700
201323.5200
201425.5400
201527.6000
201632.1100
201734.0000

## References

• Vinkler, P. (2009) The p-index: A new indicator for assessing scientific impact. Journal of Information Science 35(5):602–612.