Project description
The E-index is a bibliometric measure introduced in the paper Consistency pays off in science (2022) by ┼×. Erkol, S. Sikdar, F. Radicchi, and S. Fortunato.
What is the E-index?
The E-index of a scientist's portfolio \(\mathcal P = \{c_1, ..., c_N \}\), including N papers totaling \(C_{tot}\) citations is $$E (\mathcal P) = -\frac{1}{N}\sum_{i=1}^N c_i log \frac{c_i}{C_{tot}}$$ which is just the product of the average number of citations \(C_{avg}\) and the Shannon entropy of the citation distribution. Therefore, to have a large E-index one needs to have a high value of \(C_{avg}\), i.e., high average impact, and a high value of the citation entropy, which corresponds to a portfolio with consistent quality, as opposed to having isolated big hits standing out of a bulk of low-impact works. In our paper we have shown that the E-index is more capable at identifying future Nobelists than current metrics, like the H-index. For more technical details, see our GitHub repository.
Other Metrics
  • Number of papers: \( N = |\mathcal P| \).
  • Total citations: \( C_{tot} = \sum_i^N c_i \).
  • Average citations: \( C_{avg} = C_{tot}/N \).
  • Maximum citations: citations received by the most cited paper, \( C_{max} = max\{c_1, ... , c_N\} \).
  • H-index: Proposed by Hirsch. The largest number \(H\) of top-cited papers with at least \(H\) citations.
  • G-index: Proposed by Egghe. The largest number \(G\) of top-cited papers with at least \(G^2\) combined citations.
  • Q̃-index: A variant of Q-index proposed by Sinatra et al.. Q̃\((\mathcal P) = exp \bigg( \frac{1}{\sum_{i=1}^N \Theta (c_i)} \sum_{i=1}^N \Theta (c_i) log c_i \bigg) \), where \(\Theta (x)=1\) if \(x>0\) and \(0\) otherwise.
  • Citation moment, \( M_{\alpha} \): A parametric measure introduced in our paper that can reward both equally or unequally distributed citations across a publication portfolio \( \mathcal P \) depending on the value of \( \alpha \). We set \( \alpha=0.3 \). \( M_{\alpha} = \frac{1}{N} \sum_{i=1}^N c_i^{\alpha} \).
Data & Features
In this website, we use OpenAlex to fetch the author and publication information. The percentile information in the author page is calculated using 100,000 randomly sampled authors for each field. The authors in each sample have at least 5 publications, and their concept score (check here) for the corresponding field is greater than 50. The analysis in this website is done only on papers with a DOI. In the comparison feature, the larger metric values are shown in bold. Only the authors who are in the top 10% in their field in terms of productivity are considered for the hall of fame. The metrics of authors in the hall of fame are calculated from a snapshot of OpenAlex obtained in October 2022. The website is powered by Django, and the visualizations are created using Google Charts.
For more information, you can drop us an email at:
We thank Filippo Menczer for encouraging us to create this portal. We also thank OpenAlex for providing the data. We gratefully acknowledge the Air Force Office of Scientific Research for the financial support, under grant #FA9550-19-1-0354.