Draft:Fi-index

Fi-index tool

In 2022, the same author proposed an extension called the Fi-index tool, also published in Publishing Research Quarterly, to apply the method not to an author's entire career but to a single manuscript during the publication process.^[10] The Fi-index tool score for a given manuscript is obtained by calculating the difference between the author's Fi-index before and after the presumed publication of the article. This variant was designed to provide certification of the quality of a manuscript's reference list with respect to self-citations.

The tool provides an interpretive scale:^[10]

• 0: reference list free of self-citations;
• < 1: normal self-citing;
• 1–2: moderate self-citing;
• > 2: h-index variations and aggressive self-citing.

Fi-score

In 2024, the Fi-score was proposed as a further development, published in Publishing Research Quarterly, with a simplified formula:^[11]

${\displaystyle {\text{Fi-score}}={\frac {h{\text{-index}}^{2}}{\text{total citations}}}\times 100}$

The Fi-score evaluates the reliability of citation counts independently of self-citations, by comparing the ratio of the squared h-index to the total number of citations. The index was calculated on a sample of 194,983 researchers drawn from the database of the world's top 2% scientists published by Stanford University.^[12] Results indicate a mean Fi-score value of 25.03 with a standard deviation of 6.85; the maximum admissible value was set at approximately 32 (mean + one standard deviation).^[11]

Discussion in the scientific community

The index has been the subject of analysis and discussion in the international academic community. Mechanician Michele Ciavarella analysed the Fi-score on iMechanica, an academic portal affiliated with the Harvard School of Engineering and Applied Sciences, highlighting the correlation between high Fi-score values and high self-citation percentages, as well as the compatibility of the results with the Stanford–Ioannidis ranking. Ciavarella further observed that the Fi-score constitutes a quick tool for identifying anomalous bibliometric profiles, regardless of discipline, with a calculation far simpler than the multidimensional composite indicator of the Stanford database.^[13]

Convergence with the work of Ioannidis (Stanford)

In June 2024, Evdaimon, Ioannidis et al. proposed, as part of a large-scale study on citation orchestration conducted with Scopus data, a set of metrics to detect citation manipulation patterns.^[14] Among the indicators presented, the authors adopted the ratio of total citations to the square of the h-index — corresponding to the inverse of the Fi-score introduced by Fiorillo two years earlier — as a marker of possible small-scale orchestration.^[14][13] The independent convergence toward a mathematically equivalent indicator was noted by Ciavarella on iMechanica, who observed that the Stanford group proposed, subsequently to Fiorillo, an index substantially analogous to the inverse of the Fi-score.^[13]

Empirical applications

The Fi-index has been applied empirically by independent researchers. A 2025 study by Saputri Nur et al., published in Khizanah al-Hikmah: Jurnal Ilmu Perpustakaan, Informasi, dan Kearsipan, employed the method to analyse the self-citation practices of the ten most productive lecturers at Halu Oleo University in Indonesia, concluding that the Fi-index values fell within normal limits for all subjects examined.^[15]

The Fi-score has also been cited in the broader context of anomalous citation detection research. Ebadulla et al. (2025) referenced the Fi-score in a study on detecting anomalous self-citations using citation network analysis and large language models, published as a Springer book chapter.^[16]