Michael S. Rosenberg’s Laboratory

Computational Evolutionary Biology & Bioinformatics

E-mail: msr@asu.edu
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The adapted pure h-index (Chai et al. 2008) is very similar to the pure h-index, except that it estimates its own core rather than relying on the standard Hirsch core. For a given publication, if one wishes to assign all authors equal credit, or if one does not have information about authorship order, one can calculate an effective citation count as the number of citations divided by the square-root of the number of authors,

$$C^{*}_i = \frac{C_i}{\sqrt{A_i}}.$$

Publications are ranked according to these new citation counts and the h-equivalent value, he, is found as the largest rank for which the rank is less than the number of equivalent citations, or

$$h_e = \underset{i}{\max}\left(i \leq C^{*}_i\right).$$The adapted pure h-index is calculated by interpolating between this value and the next largest, as

$$h_{ap.\text{frac}}= \frac{\left(h_e+1\right)C^{*}_{h_e}-h_e C^{*}_{h_e +1}}{C^{*}_{h_e}-C^{*}_{h_e+1}+1}.$$

Example

Publications are ordered by adjusted number of citations, from highest to lowest.

 Citations (Ci) Authors (Ai) Adjusted Citations ($$C^*_i$$) Rank (i) 42 36 9 14 11 9 2 2 3 2 1 1 1 0 0 0 3 3 1 3 2 4 1 1 4 4 1 2 4 4 2 1 24.25 20.78 9.00 8.08 7.78 4.50 2.00 2.00 1.50 1.00 1.00 0.71 0.50 0.00 0.00 0.00 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 he = 5

The largest rank where $$i \leq C^*_i$$ is 5. Interpolating between this and the next largest rank yields hap.frac = 5.6494.

Yearhap.frac
19970.0000
19982.0617
19992.9385
20004.5000
20015.6494
20026.8000
20038.2000
200410.2736
200512.3333
200614.3333
200715.7084
200818.0000
200919.0000
201020.6694
201123.2507
201224.5000
201327.1261
201428.2905
201529.5050
201630.0093
201730.6532

References

• Chai, J.-c., P.-h. Hua, R. Rousseau, and J.-k. Wan (2008) The adapted pure h-index. Fourth International Conference on Webometrics, Informetrics and Scientometrics & Ninth COLLNET Meeting, H. Kretschmer and F. Havemann, eds. Humboldt-Universität zu Berlin: Institute for Library and Information Science.