# Michael S. Rosenberg’s Laboratory

Computational Evolutionary Biology & Bioinformatics

E-mail: msr@asu.edu
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## history h-index

The history h-index (Randić 2009) is another metric designed to help distinguish among researchers with identical h-indices. It is based on the idea of exploring a power expansion of the citation counts for publications in the core. This index starts by creating a vector representing larger power expansions of citation counts. The kth element of the vector is the largest rank (i), for which the number of citations for that publication is equal or larger than the rank times 2k, or

$$H^k=\underset{i}{\max}\left(C_i \geq i \times 2^k\right).$$

By definition, the first (zeroth) entry is h (since 20 = 1). Graphically, this is looking at the intersection (rounding the rank down to the nearest integer) of the citation curve with a series of lines with ever increasing slopes of 2k: 1 (=h), 2, 4, 8, etc., with the largest k equal to the line with the largest slope that actually intersects the citation curve.

The history h-index is simply the sum of the values in this vector, or

$$H=\sum\limits_{k=0}^{K}{H^k},$$

where K is the largest power of 2 for which Cmax >= 2K.

### Example

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

Citations (Ci)Rank (i)20212223242526
H5 = 14211248163264
H3 = 2, H4 = 2362248163264128
H2 = 31433612244896192
H1 = 411448163264128256
95510204080160320
H0 = 696612244896192384
377142856112224448
288163264128256512
299183672144288576
21010204080160320640
11111224488176352704
11212244896192384768
113132652104208416832
014142856112224448896
015153060120240480960
0161632641282565121024

The sum of all of the Hk values is 18.

YearH
19971
19984
19999
200013
200118
200222
200327
200434
200544
200650
200756
200866
200974
201078
201183
201291
201398
2014106
2015112
2016117
2017117

## References

• Randić, M. (2009) Citations versus limitations of citations: Beyond Hirsch index. Scientometrics 80(3):809–818.