Evolutionary Biological Data Science Laboratory

fractional g-index

The fractional g-index (Egghe 2008) is a variant of the g-index in which ranks are normalized by the number of authors and is the g equivalent of the h_m-index. Effective ranks for each publication are calculated identically as for h_m and g_F is calculated as:

$$g_F=\underset{r_{\text{eff}}\left(i\right)}{\max}\left(r_{\text{eff}}\left(i\right)^2 \leq \sum\limits_{j=1}^{i}{C_j}\right).$$

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
Cumulative Citations (ΣCi)	57	83	99	111	122	132	136	139	141	142	143	144	145	145	145	145	145	145
Authors (Ai)	3	3	2	3	1	4	4	4	1	4	2	1	1	4	2	1	1	1
Author Effort (Ei = 1/Ai)	0.33	0.33	0.50	0.33	1.00	0.25	0.25	0.25	1.00	0.25	0.50	1.00	1.00	0.25	0.50	1.00	1.00	1.00
Rank (i)	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18
Adjusted Rank (reff(i) = ΣEi)	0.33	0.67	1.17	1.50	2.50	2.75	3.00	3.25	4.25	4.50	5.00	6.00	7.00	7.25	7.75	8.75	9.75	10.75
Adjusted Rank Squared (reff(i)2	0.11	0.44	1.36	2.25	6.25	7.56	9.00	10.56	18.06	20.25	25.00	36.00	49.00	52.56	60.06	76.56	95.06	115.56
																		gF = 10.75

The largest adjusted rank where r_eff(i)² ≤ ΣC_i is 10.7500.

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