# Michael S. Rosenberg’s Laboratory

Computational Evolutionary Biology & Bioinformatics

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

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

$$\xi_p=\sum\limits_{i=1}^{h_p}{C^{*}_i}=\sum\limits_{i=i}^{h_p}{\frac{C_i}{\frac{A_i\left(A_i+1\right)}{2\left(A_i+1-a_i\right)}}}=\sum\limits_{i=i}^{h_p}{C_i\frac{2\left(A_i+1-a_i\right)}{A_i\left(A_i+1\right)}}.$$

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) Author Position (ai) Author Effort (Ei) Weight (wi) Adjusted Citations ($$C^*_i$$) Rank (i) 42 36 9 11 14 2 2 9 1 2 1 3 1 0 0 0 3 3 1 2 3 1 1 4 1 4 2 4 4 4 2 1 1 1 1 2 3 1 1 3 1 1 1 3 3 3 1 1 0.50 0.50 1.00 0.33 0.17 1.00 1.00 0.20 1.00 0.40 0.67 0.20 0.20 0.20 0.67 1.00 2.00 2.00 1.00 3.00 6.00 1.00 1.00 5.00 1.00 2.50 1.50 5.00 5.00 5.00 1.50 1.00 21.00 18.00 9.00 3.67 2.33 2.00 2.00 1.80 1.00 0.80 0.67 0.60 0.20 0.00 0.00 0.00 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 hp = 3

The sum of the adjusted citations for the top hp publications is 48.0.

Yearξp
19970.0000
19983.0000
199911.5000
200018.5000
200148.0000
200294.6667
2003150.5000
2004239.1667
2005349.3333
2006481.0952
2007634.1310
2008789.4881
2009992.6429
20101202.7500
20111405.4405
20121571.9286
20131764.2381
20141967.5833
20152131.5595
20162298.8929
20172426.6429

## References

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