# Michael S. Rosenberg’s Laboratory

Computational Evolutionary Biology & Bioinformatics

E-mail: msr@asu.edu
← Back to introduction

## pure h-index (geometric 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 geometric assignment of credit for each publication as:

$$E_i=\frac{2^{A_i - a_i}}{2^{A_i} - 1},$$

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:

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

### 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 0.57 0.57 0.14 0.33 0.13 1.00 0.13 0.53 1.00 1.00 0.13 0.67 1.00 0.13 0.67 1.00 1.75 1.75 7.00 3.00 7.50 1.00 7.50 1.88 1.00 1.00 7.50 1.50 1.00 7.50 1.50 1.00

The h-index is 6 and the sum of the weights for the publications in the core is 22.0, thus hp.geom = 3.1334.

Yearhp.geom
19970.7559
19981.2978
19991.5159
20002.4398
20013.1334
20023.8204
20035.3015
20041.4889
20051.9089
20062.3513
20072.8312
20083.3323
20094.4097
20104.6934
20115.2816
20125.2130
20135.5592
20146.3998
20157.0003
20167.2775
20177.2775

## 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.