# Michael S. Rosenberg’s Laboratory

Computational Evolutionary Biology & Bioinformatics

E-mail: msr@asu.edu
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## position-weighted h-index

The position-weighted h-index (Abbas 2011) is similar to the adapted pure h-index with proportional weighting in that it uses an author's position to weight citation counts prior to ranking, but differs by dividing the raw citation count directly by the inverse of the effort rather than the square-root of the effort. The effort is calculated as

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

with weight wi = 1/Ei, and the adjusted citation count as

$$C^{*}_i = \frac{C_i}{w_i} = C_i E_i,$$

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). Publications are ranked by these adjusted citation counts and then the metric is calculated as:

$$h_p=\underset{i}{\max}\left(i \leq C^{*}_i\right).$$

### Example

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

 Citations (Ci) Authors (Ai) Author Position (ai) Author Effort (Ei) Weight (wi) Adjusted Citations ($$C^*_i$$) Rank (i) 42 36 9 11 14 2 2 9 1 2 1 3 1 0 0 0 3 3 1 2 3 1 1 4 1 4 2 4 4 4 2 1 1 1 1 2 3 1 1 3 1 1 1 3 3 3 1 1 0.50 0.50 1.00 0.33 0.17 1.00 1.00 0.20 1.00 0.40 0.67 0.20 0.20 0.20 0.67 1.00 2.00 2.00 1.00 3.00 6.00 1.00 1.00 5.00 1.00 2.50 1.50 5.00 5.00 5.00 1.50 1.00 21.00 18.00 9.00 3.67 2.33 2.00 2.00 1.80 1.00 0.80 0.67 0.60 0.20 0.00 0.00 0.00 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 hp = 3

The largest rank where $$i \leq C^*_i$$ is 3.

Yearhp
19970
19981
19992
20002
20013
20025
20036
20048
200510
200611
200713
200814
200916
201017
201119
201220
201321
201422
201522
201622
201722

## References

• Abbas, A.M. (2011) Weighted indices for evaluating the quality of research with multiple authorship. Scientometrics 88:107–131.