Michael S. Rosenberg’s Laboratory

Computational Evolutionary Biology & Bioinformatics

E-mail: msr@asu.edu
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hm-index

While the normalized hi-index accounts for the number of authors of a publication by normalizing the citation count for that publication, hm (Schreiber 2008), also known as the fractional paper h and hF-index (Egghe 2008), accounts for author number by normalizing the ranks. For this index, one counts the number of citations and ranks the publications as for the h-index, but rather than counting the rank of the ith publication as i, it is instead calculated as the cumulative sum of 1/Ai. In formal terms, when calculating the h-index the rank of the ith publication is

$$r_i=\sum\limits_{j=1}^{i}{1}=i.$$

For hm we instead calculate the effective rank as

$$r_{\text{eff}}\left(i\right)=\sum\limits_{j=1}^{i}{\frac{1}{A_i}}.$$

hm is determined as the largest value of reff(i) for which reff(i) ≤ Ci or

$$h_m=\underset{r_{\text{eff}}\left(i\right)}{\max}\left(r_{\text{eff}}\left(i\right) \leq C_i\right).$$

Example

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

Citations (Ci)42361411993222111000
Authors (Ai)3332414411421421
Author Effort (Ei = 1/Ai)0.330.330.330.500.251.000.250.251.001.000.250.501.000.250.501.00
Rank (i)12345678910111213141516
Adjusted Rank (reff(i) = ΣEi)0.330.671.001.501.752.753.003.254.255.255.506.007.007.257.758.75
hm = 3.00

The largest adjusted rank where reff(i) ≤ Ci is 3.0000.

History

Yearhm
19970.5833
19981.1667
19991.4167
20002.7500
20013.0000
20024.2500
20035.6706
20047.6706
20059.2615
200610.5949
200712.6782
200813.4282
200914.6782
201016.5191
201117.3941
201217.5767
201318.5767
201418.5767
201518.8267
201618.8267
201718.9695

References