# Michael S. Rosenberg’s Laboratory

Computational Evolutionary Biology & Bioinformatics

E-mail: msr@asu.edu
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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) Cumulative Citations (ΣCi) Authors (Ai) Author Effort (Ei = 1/Ai) Rank (i) Adjusted Rank (reff(i) = ΣEi) Adjusted Rank Squared (reff(i)2 42 36 14 11 9 9 3 2 2 2 1 1 1 0 0 0 42 78 92 103 112 121 124 126 128 130 131 132 133 133 133 133 3 3 3 2 4 1 4 4 1 1 4 2 1 4 2 1 0.33 0.33 0.33 0.50 0.25 1.00 0.25 0.25 1.00 1.00 0.25 0.50 1.00 0.25 0.50 1.00 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 0.33 0.67 1.00 1.50 1.75 2.75 3.00 3.25 4.25 5.25 5.50 6.00 7.00 7.25 7.75 8.75 0.11 0.44 1.00 2.25 3.06 7.56 9.00 10.56 18.06 27.56 30.25 36.00 49.00 52.56 60.06 76.56 gF = 8.75

The largest adjusted rank where reff(i)2 ≤ ΣCi is 8.7500.

YeargF
19971.1667
19982.6667
19992.9167
20005.7500
20018.7500
200210.1706
200311.5949
200413.0949
200517.4282
200617.9282
200719.2615
200819.7949
200922.5449
201024.1100
201125.6933
201226.0267
201327.8219
201429.8219
201530.2719
201630.8969
201731.1648

## References

• Egghe, L. (2008) Mathematical theory of the h- and g-index in case of fractional counting of authorship. Journal of the American Society for Information Science and Technology 59(10):1608–1616.