# Michael S. Rosenberg’s Laboratory

Computational Evolutionary Biology & Bioinformatics

E-mail: msr@asu.edu
← Back to introduction

## b-index (10% 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 simply assume a self-citation rate of 10%, meaning the non-self-citation rate is 90%, or k = 0.9.

Yearb10%
19970.9240
19981.8480
19992.7721
20004.6201
20015.5441
20026.4681
20038.3162
200410.1642
200512.0123
200613.8603
200715.7084
200817.5564
200921.2525
201022.1765
201124.0245
201224.9486
201326.7966
201429.5687
201531.4167
201632.3407
201732.3407

## 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.