Consistency pays off in science

This repository contains the code for Consistency pays off in science (2023), Ş. Erkol, S. Sikdar, F. Radicchi, and S. Fortunato. Quantitative Science Studies.

• Paper
• arXiv preprint
• Website

Classification

The notebook classification.ipynb can be used to replicate the full portfolio classification results for Chemistry.

Citation Moment and E-index

We propose two measures for identifying excellence in science:

• Citation moment $\left(M_\alpha\right)$
• E-index

Citation Moment $\left(M_\alpha\right)$

A parametric measure that can potentially reward different types of publication portfolios $\mathcal P$ depending on the value of the parameter $\alpha$.

$$M_\alpha\left(\mathcal P\right) = \frac{1}{N} \sum_{i=1}^N c_i^{\alpha}$$

E-index

A parameter-free measure sensitive to the distribution of citations, favoring portfolios with citations distributed equally among papers.

$$E\left(\mathcal P\right) = -\frac{1}{N} \sum_{i=1}^N c_i log\frac{c_i}{C_{tot}}$$

This measure is the product of average citations $\left(C_{avg}\right)$ and Shannon entropy of the citation distribution.

Symbols

• $c_i$: citations received by publication $i$
• $\mathcal P$: publication portfolio of a scientist, $\mathcal P = \{c_1, c_2, ..., c_N \}$
• $N = |\mathcal P|$
• $C_{tot} = \sum_i c_i$
• $C_{avg} = \frac{C_{tot}}{N}$

Other measures

The repository includes functions for calculating some other measures, such as H-index (Hirsch), G-index (Egghe), and Q-index (Sinatra et al.).

E-index portal

We have created the portal e-index.net! You can use the website to search for scientists and see their citation measures, including E-index. You can compare the measures of two different scientists, and see how they rank in their field. You can also check the hall of fame in each field for various citation measures. We use OpenAlex API to fetch the portfolios of scientists.