# Michael S. Rosenberg’s Laboratory

Computational Evolutionary Biology & Bioinformatics

E-mail: msr@asu.edu
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## pure h-index (proportional credit)

The pure h-index (Wan et al. 2007) is similar to the hi-index in that it attempts to adjust for multiple authors. The index allows for different methods of assigning authorship credit. If one has information on author order and assumes the order directly correlates with effort, one can use a proportional (artihmetic) assignment of credit for each publication as:

$$E_i=\frac{2\left(A_i + 1 - a_i\right)}{A_i\left(A_i + 1\right)},$$

where ai is the position of the target author within the full author list of publication i (i.e., an integer from 1 to Ai). Each publication can then be weighted by the inverse of the author effort, wi = 1/Ei. Given the credited effort for each publication, the metric is calculated as:

$$h_{p.\text{prop}}=\frac{h}{\sqrt{\frac{\sum\limits_{i=1}^{h}{w_i}}{h}}}.$$

### Example

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

 Citations (Ci) Rank (i) Authors (Ai) Author Position (ai) Author Effort (Ei) Weight (wi) 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 h = 6 3 3 3 2 4 1 4 4 1 1 4 2 1 4 2 1 1 1 3 2 3 1 3 1 1 1 3 1 1 3 1 1 0.50 0.50 0.17 0.33 0.20 1.00 0.20 0.40 1.00 1.00 0.20 0.67 1.00 0.20 0.67 1.00 2.00 2.00 6.00 3.00 5.00 1.00 5.00 2.50 1.00 1.00 5.00 1.50 1.00 5.00 1.50 1.00

The h-index is 6 and the sum of the weights for the publications in the core is 19.0, thus hp.prop = 3.3717.

Yearhp.prop
19970.7071
19981.2649
19991.5667
20002.6352
20013.3717
20024.0904
20035.6177
20043.8542
20054.8841
20065.7607
20076.8666
20087.9254
200910.1889
201010.7466
201111.9929
201211.7681
201312.5691
201414.0233
201515.2670
201615.7142
201715.7142

## References

• Wan, J.-k., P.-h. Hua, and R. Rousseau (2007) The pure h-index: Calculating an author's h-index by taking co-authors into account. Collnet Journal of Scientometrics and Information Management 1(2):1–5.