# Michael S. Rosenberg’s Laboratory

Computational Evolutionary Biology & Bioinformatics

E-mail: msr@asu.edu
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## w-index (Woeginger)

Woeginger's w-index (Woeginger 2008) is somewhat similar to the h-index. It is the largest value of w for which publications have at least 1, 2, 3, …w citations:

$$w=\underset{k}{\max}\left(C_i \geq k-i+1\right),$$

for all ik. Put another way, the top 1…k publications have to have at least k…1 citations, respectively.

Graphically, if the h-index is the largest square with sides h that can fit under the citation curve, w is the largest right-angled isoceles triangle with perpendicular sides of w.

### Example

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

Citations (Ci) Rank (k) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 42 36 14 11 9 9 3 2 2 2 1 1 1 0 0 0 k…1 1 2 1 3 2 1 4 3 2 1 5 4 3 2 1 6 5 4 3 2 1 7 6 5 4 3 2 1 8 7 6 5 4 3 2 1 w = 9 9 8 7 6 5 4 3 2 1 10 9 8 7 6 5 4 3 2 1 11 10 9 8 7 6 5 4 3 2 1 12 11 10 9 8 7 6 5 4 3 2 1 13 12 11 10 9 8 7 6 5 4 3 2 1 14 13 12 11 10 9 8 7 6 5 4 3 2 1 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

The largest rank where the minimum number of citations for publications 1…kk…1 is 9.

Yearw
19971
19984
19995
20008
20019
200213
200317
200422
200525
200629
200732
200835
200935
201040
201142
201244
201345
201446
201547
201649
201749

## References

• Woeginger, G.J. (2008) An axiomatic characterization of the Hirsch-index. Mathematical Social Sciences 56(2):224–242.