Michael S. Rosenberg’s Laboratory

Computational Evolutionary Biology & Bioinformatics

E-mail: msr@asu.edu
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f-index (Tol)

If the h- and g-indices are the largest value x for which x publications have a minimum (h) or mean (g) number of citations equal to x, then Tol's f-index (Tol 2007) is the same idea, except based on the harmonic mean number of citations for the top f publications.

$$f=\underset{i}{\max}\left(\frac{1}{\frac{1}{i}\sum\limits_{j=1}^{i}{\frac{1}{C_j}}}\geq i\right)=\underset{i}{\max}\left(\frac{i}{\sum\limits_{j=1}^{i}{\frac{1}{C_j}} }\geq i\right)$$

Example

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

Citations (Ci)42361411993222111000
Rank (i)12345678910111213141516
Harmonic Mean Citations42.038.824.418.715.413.89.16.35.14.43.42.82.52.72.83.0
f = 7

The largest rank where i ≤ harmonic mean citations is 7.

History

Yearf
19971
19983
19994
20006
20017
20029
200312
200416
200518
200621
200724
200827
200930
201032
201135
201237
201338
201439
201540
201641
201742

References