Evolutionary Biological Data Science Laboratory

weighted citation H-cut (proportional)

The proportional weighted citation H-cut is the sum of weighted citations found within an author's core publications, with the core defined by the position-weighted h-indexand the citation weighting using the scheme from the weighted citation aggregate (proportional):

$$\xi_p=\sum\limits_{i=1}^{h_p}{C^{*}_i}=\sum\limits_{i=i}^{h_p}{\frac{C_i}{\frac{A_i\left(A_i+1\right)}{2\left(A_i+1-a_i\right)}}}=\sum\limits_{i=i}^{h_p}{C_i\frac{2\left(A_i+1-a_i\right)}{A_i\left(A_i+1\right)}}.$$

Note that for this metric publication order is by the weighted citation counts rather than the raw citation counts.

Example

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

Citations (Ci)	57	11	12	16	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 (\(C^*_i\))	28.50	11.00	6.00	5.33	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 sum of the adjusted citations for the top h_p publications is 50.833333333333336.

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