# Michael S. Rosenberg’s Laboratory

Computational Evolutionary Biology & Bioinformatics

E-mail: msr@asu.edu
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## EM′-index

The EM′-index (Bihari and Tripathi 2017) is an extension of the EM-index which includes all publications, rather than just those from the core. Like the EM-index, we begin by creating a vector (E) where the first value is E1 = h. Subsequent values of the vector, Ei+1, are determined by subtracting Ei from the citation count for all publications in the core defined by Ei, and recalculating h from these new citation counts, reranking all publications by these new citation counts as necessary (i.e., some of the publications previously in the tail of the citation distribution may advance beyond publications in the core as citaions representing earlier calculations of h are “used up”). This process continues until one runs out of citations, all of the remaining publications have only a single remaining citation, or there is only a single publication left to be considered. From this vector, one calculates the index as:

$$EM^\prime=\sqrt{\sum\limits_{i=1}^{n}{E_i}},$$

where Ei and n are the ith element and length of E, respectively.

### Example

Publications are ordered by number of citations, from highest to lowest. After each step, Ei is substracted from the citations of the top Ei publications and all publications are re-ranked by this adjusted citation count for the next step.

Citations (Ci) Rank (i) Adjusted Citations (Ci) New Rank (i) Adjusted Citations (Ci) New Rank (i) Adjusted Citations (Ci) New Rank (i) 42 36 14 11 9 9 3 2 2 2 1 1 1 0 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 E1 = 6 36 30 8 5 3 3 3 2 2 2 1 1 1 0 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 E2 = 4 32 26 4 3 3 3 2 2 2 1 1 1 1 0 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 E3 = 3 29 23 3 3 3 2 2 2 1 1 1 1 1 0 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 E4 = 3 26 20 3 3 2 2 2 1 1 1 1 1 0 0 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 E5 = 3 23 17 3 2 2 2 1 1 1 1 1 0 0 0 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 E6 = 3 20 14 2 2 2 1 1 1 1 1 0 0 0 0 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 E7 = 2 18 12 2 2 2 1 1 1 1 1 0 0 0 0 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 E8 = 2 16 10 2 2 2 1 1 1 1 1 0 0 0 0 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 E9 = 2 14 8 2 2 2 1 1 1 1 1 0 0 0 0 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 E10 = 2 12 6 2 2 2 1 1 1 1 1 0 0 0 0 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 E11 = 2 10 4 2 2 2 1 1 1 1 1 0 0 0 0 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 E12 = 2 8 2 2 2 2 1 1 1 1 1 0 0 0 0 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 E13 = 2 6 2 2 2 1 1 1 1 1 0 0 0 0 0 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 E14 = 2 4 2 2 1 1 1 1 1 0 0 0 0 0 0 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 E15 = 2 2 2 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 E16 = 2 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 E17 = 1

The sum of the 17 E values is 43. The EM′-index is the square-root of this sum, thus EM′ = 6.5574.

YearEM
19971.0000
19982.4495
19994.3589
20004.3589
20016.5574
20029.4340
200311.9164
200414.7309
200517.2337
200619.4165
200722.0454
200824.6171
200927.3496
201029.6985
201131.9218
201232.9090
201333.8378
201435.0000
201535.9444
201637.1618
201737.9078

## References

• Bihari, A., and S. Tripathi (2017) EM-index: A new measure to evaluate the scientific impact of scientists. Scientometrics 112(1):659–677.