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
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We thank Filippo Menczer for encouraging us to create this portal. We also thank Clarivate for providing the data. We gratefully acknowledge the Air Force Office of Scientific Research for the financial support, under grant #FA9550-19-1-0354.