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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)572616121110432111100000
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 = 111/100 = 1.11.

History

Yearπ
19970.0200
19980.0900
19990.3700
20000.5900
20011.1100
20021.7100
20032.7500
20043.8000
20055.5100
20068.5800
200711.1500
200813.4300
200915.8300
201020.3500
201123.0900
201226.4100
201329.3400
201435.5300
201539.2200
201643.3300
201747.0500
201850.7500
201954.3200
202057.8700
202161.4000
202269.6700
202373.3800
202477.3700
202578.1500

References