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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)592616111110433211100000
Rank (i)123456789101112131415161718
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

Yearπ
19970.0200
19980.1000
19990.3700
20000.6000
20011.1200
20021.7200
20032.7200
20043.8100
20055.5300
20068.5500
200711.1700
200813.4900
200915.9100
201020.4100
201123.1300
201226.4000
201329.3700
201435.6500
201539.3500
201643.4700
201747.1600
201850.8400
201954.3800
202057.9900
202161.4500
202269.8600
202373.5500
202477.3700
202579.1600

References