# Michael S. Rosenberg’s Laboratory

Computational Evolutionary Biology & Bioinformatics

E-mail: msr@asu.edu
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## b-index (mean self-citation rate)

The b-index (Brown 2009) is designed to correct h for self-citations, without actually having to check the citation records for every publication. It assumes that an author's self-citation rate is fairly consistent across publications such that, on average, a fraction k of the citations are from other authors. Assuming that citations follow a Zipfian distribution and that empirically derived estimates of the shape of this distribution are reasonable, one finds the index

$$b=hk^{\frac{3}{4}},$$

where b is an estimate of the h-index corrected for self-citations.

There are multiple ways to estimate the non-self-citation rate (k). In this case, we calculate it directly as the mean of the proportion of self-citations to total-citations across all publication, subtracted from one, or

$$k=1-\bar{S_r}=1-\frac{\sum\limits_{i=1}^{P}{\frac{s_i}{C_i}}}{P}$$

where si is the number of self-citations by the target author to the ith publication.

Yearbmean.self
19970.6817
19981.7006
19992.4856
20004.2007
20015.0947
20025.3923
20037.9068
20049.9329
200511.2363
200613.5443
200715.4022
200817.6738
200921.1070
201022.3004
201123.9925
201224.6977
201327.2169
201429.7429
201531.9200
201632.9506
201732.6308

## References

• Brown, R.J.C. (2009) A simple method for excluding self-citation from the h-index: the b-index. Online Information Review 33(6):1129–1136.