Evolutionary Biological Data Science Laboratory

adapted pure h-index (fractional credit)

The adapted pure h-index (Chai et al. 2008) is very similar to the pure h-index (fractional credit), except that it estimates its own core rather than relying on the standard h-index core. For a given publication, if one wishes to assign all authors equal credit, or if one does not have information about authorship order, one can calculate an effective citation count as the number of citations divided by the square-root of the number of authors,

$$C^{*}_i = \frac{C_i}{\sqrt{A_i}}.$$

Publications are ranked according to these new citation counts and the h-equivalent value, h_e, is found as the largest rank for which the rank is less than the number of equivalent citations, or

$$h_e = \underset{i}{\max}\left(i \leq C^{*}_i\right).$$The adapted pure h-index is calculated by interpolating between this value and the next largest, as

$$h_{ap.\text{frac}}= \frac{\left(h_e+1\right)C^{*}_{h_e}-h_e C^{*}_{h_e +1}}{C^{*}_{h_e}-C^{*}_{h_e+1}+1}.$$

Example

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

Citations (Ci)	59	26	16	11	11	10	3	4	3	2	1	1	1	0	0	0	0	0
Authors (Ai)	3	3	2	1	3	4	1	4	4	4	1	1	2	4	2	1	1	1
Adjusted Citations (\(C^*_i\))	34.06	15.01	11.31	11.00	6.35	5.00	3.00	2.00	1.50	1.00	1.00	1.00	0.71	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
					he = 5

The largest rank where \(i \leq C^*_i\) is 5. Interpolating between this and the next largest rank yields h_ap.frac = 5.5746.

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