Evolutionary Biological Data Science Laboratory

b-index (mean self-citation rate)

The b-index (Brown 2009) is designed to correct the h-index 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 s_i is the number of self-citations by the target author to the i^th publication.

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