Evolutionary Biological Data Science Laboratory

position-weighted h-index

The position-weighted h-index (Abbas 2011) is similar to the adapted pure h-index (proportional credit) 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 w_i = 1/E_i, and the adjusted citation count as

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

where a_i is the position of the target author within the full author list of publication i (i.e., an integer from 1 to A_i). 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)	47	11	19	15	26	10	2	4	1	1	1	3	1	0	0	0	0	0
Authors (Ai)	3	1	3	2	3	4	1	4	1	1	2	4	4	4	2	1	1	1
Author Position (ai)	1	1	1	2	3	3	1	1	1	1	1	3	3	3	1	1	1	1
Author Effort (Ei)	0.50	1.00	0.50	0.33	0.17	0.20	1.00	0.40	1.00	1.00	0.67	0.20	0.20	0.20	0.67	1.00	1.00	1.00
Weight (wi)	2.00	1.00	2.00	3.00	6.00	5.00	1.00	2.50	1.00	1.00	1.50	5.00	5.00	5.00	1.50	1.00	1.00	1.00
Adjusted Citations (\(C^*_i\))	23.50	11.00	9.50	5.00	4.33	2.00	2.00	1.60	1.00	1.00	0.67	0.60	0.20	0.00	0.00	0.00	0.00	0.00
Rank (i)	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18
				hp = 4

The largest rank where \(i \leq C^*_i\) is 4.

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