# Michael S. Rosenberg’s Laboratory

Computational Evolutionary Biology & Bioinformatics

E-mail: msr@asu.edu
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## pure h-index (fractional 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 wishes to assign all authors equal credit, or if one does not have information about authorship order, one can assign fractional credit per author, which essentially means this metric is simply the h-index divided by the square-root of the average number of authors in the core, thus differing from hi only by the square-root in the denominator (which makes the fractional version of the pure h-index less harsh than hi by not punishing co-authorship as severely).

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

### Example

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

 Citations (Ci) Rank (i) Authors (Ai) 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

The h-index is 6 and the sum of the authors for publications in the core is 16, thus hi = 3.6742.

Yearhp.frac
19970.5774
19981.2649
19991.8371
20002.8868
20013.6742
20024.3653
20035.6299
20045.8419
20057.2325
20067.7632
20079.1253
200810.3524
200913.1839
201013.6679
201115.1083
201214.4704
201315.3137
201416.3220
201517.7322
201618.2309
201718.2309

## 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.