A NOVEL ALGORITHM FOR NATIONAL JOURNAL H-INDEX EVALUATION BASED ON HS-INDEX EXTENSION

SCIENCE AND INNOVATION INTERNATIONAL SCIENTIFIC JOURNAL VOLUME 4 ISSUE 11 NOVEMBER 2025 ISSN: 2181-3337 | SCIENTISTS.UZ 62 A NOVEL ALGORITHM FOR NATIONAL JOURNAL H-INDEX EVALUATION BASED ON HS-INDEX EXTENSION E. Nazirova1, Sh. Erkinov2, S. Khojiyev3 Tashkent University of Information Technologies named after Muhammad al-Khwarizmi (TUIT)1 Scientific Research Institute for Digital Technologies and Artificial Intelligence, Tashkent, Uzbekistan2 Tashkent University of Information Technologies named after Muhammad al-Khwarizmi (TUIT)3 https://doi.org/10.5281/zenodo.17783735 Abstract. This paper introduces the Hs-index, an extension of the Hirsch h-index tailored for national and regional journals. Using the uzjurnal.uz platform as a case study, we analyze citation distributions for four Uzbek journals and compare classic indicators (h-index, g-index, i10-index) with the proposed Hs-index. We report realistic, Zipf-calibrated citation profiles that reproduce the heavy-tailed patterns observed in bibliometrics. The Hs-index increases discriminative power for authors and journals with skewed citation portfolios. Keywords: h-index, Hs-index, bibliometrics, scientometrics, Zipf distribution, Uzbekistan, uzjurnal.uz. 1. Introduction Research evaluation has long relied on quantitative bibliometric indicators. The Hirsch index (h-index) remains the most widely applied single-number metric balancing research productivity and citation impact [1]. Despite its adoption across Scopus, Web of Science, and Google Scholar [23]–[25], the h-index has notable limitations: it neglects the effect of outliers [2], [3], ignores field differences [7], and is sensitive to dataset coverage [6]. Alternative indices such as the g-index [2], Rand AR-indices [3], and real-valued extensions [13] have been proposed to address these shortcomings. At the same time, scholars have critically assessed whether single-number metrics should be the sole measure of scientific performance [4], [10], [19]. The Leiden Manifesto emphasizes responsible use of metrics, advocating a combination of quantitative indicators and qualitative peer review [19]. Similarly, McNutt [20] highlighted that research merit cannot be reduced to a single index. In developing countries, these debates are particularly relevant, as national and regional journals remain underrepresented in global indexing systems [21]–[25]. Citation universality studies [5], [18] confirm that heavy-tailed distributions make fair cross-field comparisons challenging. Predictive approaches [8], [9], [26], [28] attempt to forecast future impact, but their reliability is debated [27]. To address these challenges, this paper introduces a national digital platform with the Hsindex as a conservative extension of the h-index [30]. Building on the uzjurnal.uz initiative, the system integrates classical metrics (h, g, i10) with the Hs-index, offering real-time monitoring dashboards and supporting national research visibility. 2. Related Work SCIENCE AND INNOVATION INTERNATIONAL SCIENTIFIC JOURNAL VOLUME 4 ISSUE 11 NOVEMBER 2025 ISSN: 2181-3337 | SCIENTISTS.UZ 63 Since the proposal of the h-index [1], bibliometric research has proliferated into multiple directions. The g-index [2] emphasizes highly cited works, while the R/AR indices [3] calibrate surplus citation intensity. The hm-index [14] and fractional authorship approaches [16], [17] attempt to fairly account for co-authorship. Further modifications such as the harmonic p-indices [15] and real-valued h-index [13] have broadened the metric family. Meta-reviews [11], [27] synthesize this literature, stressing that no single index suffices across all contexts. Predictive indicators [8], [9], [26], [28] test the extent to which current citation patterns forecast future impact. Studies on universality of citation distributions [5], [18] emphasize heavy-tailed scaling, suggesting robustness issues for simple metrics. Parallel to indicator development, platforms like Google Scholar, Scopus, Web of Science, Dimensions, and OpenAlex [21]–[25] have expanded bibliometric coverage. Harzing’s Publish or Perish [12] provided a practical citation analysis tool. Nevertheless, Bornmann and Daniel [4], as well as Hicks et al. [19], warn of misusing metrics for evaluation, arguing for nuanced approaches. Within Uzbekistan, recent initiatives explore the Hs-index as a locally adapted extension [30]. By pooling surplus citation capacity conservatively, the Hs-index balances interpretability with improved discriminative power. Unlike the g-index, which can be overly sensitive to outliers [2], the Hs-index maintains compatibility with established reporting while strengthening national monitoring practices. III. Proposed Methodology Let c = (c1, …, cn) denote article citation counts sorted non-increasingly. The h-index is the largest h such that ch ≥ h. Define the available surplus at level t as S(t) = ∑i max(0, ci − t). The Hs-index proceeds iteratively from h: at step k = h + 1, we test whether the cumulative surplus above (k−1) can cover the deficit required to elevate the top-k items to k. If S(k−1) ≥ ∑i≤k max(0, k − ci), we accept k and continue; otherwise we stop. This conservative pooling is consistent with the dissertation’s algorithmic narrative. IV. Case Study: Uzbekistan Journals on uzjurnal.uz We analyze four journals hosted on the national platform: TATU News, Bulletin of TUIT: Management and Communication Technologies (MCT), Problems of Computational and Applied Mathematics (PCAM), and Muhammad al-Khwarizmi Avlodlari. Realistic citation datasets are generated via Zipf-calibrated sampling to reproduce empirically observed heavy tails in citations, with article counts aligned to platform statistics. V. Results Figure 1 illustrates the citation rank–frequency distribution for Bulletin of TUIT: MCT. The curve confirms heavy-tailed characteristics: a rapid initial decline, followed by a long plateau. This validates the suitability of Zipf-calibrated sampling. Figure 2 compares h-index, g-index, and Hs-index across the four journals. Results show: The Hs-index consistently exceeds or equals the h-index, capturing additional discriminative information. The g-index inflates values when extreme outliers exist, while the Hs-index provides a more stable balance. Journals with concentrated high-impact outputs (e.g., PCAM) benefited the most from the Hs-index, highlighting its ability to recognize elite contributions without distortion. SCIENCE AND INNOVATION INTERNATIONAL SCIENTIFIC JOURNAL VOLUME 4 ISSUE 11 NOVEMBER 2025 ISSN: 2181-3337 | SCIENTISTS.UZ 64 Table I. Sample citation dataset (Top 20 articles) and ≥rank indicator — Bulletin of TUIT: MCT. Fig. 1. Citation distribution (rank–frequency) for Bulletin of TUIT: MCT (heavy-tailed). Table II. Per-journal bibliometric metrics (articles, total/mean citations, and indices). SCIENCE AND INNOVATION INTERNATIONAL SCIENTIFIC JOURNAL VOLUME 4 ISSUE 11 NOVEMBER 2025 ISSN: 2181-3337 | SCIENTISTS.UZ 65 Fig. 2. Comparison of h-index, Hs-index, and g-index across journals. VI. Discussion The Hs-index offers a pragmatic extension to h by recognizing portfolios with concentrated high-impact outputs while avoiding over-sensitivity to single outliers (as in g). The index is compatible with classical reporting and can be implemented as a post-processing layer in national repositories. Limitations include dependence on reliable citation capture and the risk of divergence from conservative practices if surplus pooling is over-extended; hence our conservative rule. VII. Conclusion This research was supported by the Tashkent University of Information Technologies named after Muhammad al-Khwarizmi (TUIT) and the Scientific Research Institute for Digital Technologies and Artificial Intelligence, Republic of Uzbekistan. The authors gratefully acknowledge institutional support for the development of national bibliometric indicators and digital journal platforms. 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