# Michael S. Rosenberg’s Laboratory

Computational Evolutionary Biology & Bioinformatics

E-mail: msr@asu.edu
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## weighted citation H-cut (fractional)

The fractional weighted citation H-cut is the sum of weighted citations found within an author's core publications, with the core defined by the normalized hi-index and the citation weighting using the scheme from the fractional weighted citation aggregate:

$$\xi_e=\sum\limits_{i=i}^{h_{i\text{-norm}}}{\frac{C_i}{A_i}}.$$

Note that for this metric publication order is by the weighted citation counts rather than the raw citation counts.

### Example

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

 Citations (Ci) Authors (Ai) Adjusted Citations (Ci/Ai) Rank (i) 42 36 9 11 14 9 2 2 1 3 2 1 1 0 0 0 3 3 1 2 3 4 1 1 1 4 4 2 4 4 2 1 14.00 12.00 9.00 5.50 4.67 2.25 2.00 2.00 1.00 0.75 0.50 0.50 0.25 0.00 0.00 0.00 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 hi-norm = 4

The sum of the adjusted citations for the top hi-norm publications is 40.5.

Yearξe
19970.0000
19982.0000
19999.0000
200018.0000
200140.5000
200277.5000
2003120.8333
2004184.6667
2005275.0000
2006393.9762
2007523.9048
2008662.3571
2009865.2143
20101082.2222
20111225.8968
20121393.1984
20131572.8571
20141760.0000
20151912.2143
20162089.2143
20172206.6587

## References

• Abbas, A.M. (2011) Weighted indices for evaluating the quality of research with multiple authorship. Scientometrics 88:107–131.