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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 hm-index. Effective ranks for each publication are calculated identically as for hm and gF 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)472619151110432111100000
Cumulative Citations (ΣCi)477392107118128132135137138139140141141141141141141
Authors (Ai)333214441421142111
Author Effort (Ei = 1/Ai)0.330.330.330.501.000.250.250.251.000.250.501.001.000.250.501.001.001.00
Rank (i)123456789101112131415161718
Adjusted Rank (reff(i) = ΣEi)0.330.671.001.502.502.753.003.254.254.505.006.007.007.257.758.759.7510.75
Adjusted Rank Squared (reff(i)20.110.441.002.256.257.569.0010.5618.0620.2525.0036.0049.0052.5660.0676.5695.06115.56
gF = 10.75

The largest adjusted rank where reff(i)2 ≤ ΣCi is 10.7500.

History

YeargF
19970.5000
19983.4167
19994.9167
20007.7500
200110.7500
200212.1706
200313.5949
200415.0949
200520.4282
200620.9282
200722.2615
200822.7949
200925.5449
201027.1100
201128.6933
201229.0267
201330.8219
201432.8219
201534.2719
201634.8969
201735.0219
201836.6398
201937.6398
202038.6398
202139.0064
202239.9333
202339.9366
202440.9366

References