Evolutionary Biological Data Science Laboratory

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 i ≤ k. 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 which fits under the curve.

Example

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

	Citations (Ci)	57	26	16	12	11	10	4	3	2	1	1	1	1	0	0	0	0	0
	Rank (k)	k…1
	1	1
	2	2	1
	3	3	2	1
	4	4	3	2	1
	5	5	4	3	2	1
	6	6	5	4	3	2	1
	7	7	6	5	4	3	2	1
	8	8	7	6	5	4	3	2	1
	9	9	8	7	6	5	4	3	2	1
w = 10	10	10	9	8	7	6	5	4	3	2	1
	11	11	10	9	8	7	6	5	4	3	2	1
	12	12	11	10	9	8	7	6	5	4	3	2	1
	13	13	12	11	10	9	8	7	6	5	4	3	2	1
	14	14	13	12	11	10	9	8	7	6	5	4	3	2	1
	15	15	14	13	12	11	10	9	8	7	6	5	4	3	2	1
	16	16	15	14	13	12	11	10	9	8	7	6	5	4	3	2	1
	17	17	16	15	14	13	12	11	10	9	8	7	6	5	4	3	2	1
	18	18	17	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…k ≤ k…1 is 10.

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