--- name: h-index-guide-9977a02bc2f1 description: "Understanding and calculating research impact metrics" metadata: openclaw: emoji: "🏅" category: "literature" subcategory: "metadata" keywords: ["h-index", "impact factor", "bibliometrics", "academic metrics", "citation statistics"] source: "wentor-research-plugins" --- # H-Index and Research Impact Metrics Guide Understand, calculate, and responsibly interpret bibliometric indicators including h-index, impact factor, and related metrics. ## Core Bibliometric Indicators ### H-Index The h-index (Hirsch index) is defined as: a researcher has an h-index of h if h of their papers have each been cited at least h times. **Example**: If a researcher has published 20 papers with citation counts [120, 80, 55, 40, 22, 18, 15, 12, 10, 8, 5, 3, 2, 2, 1, 1, 0, 0, 0, 0], their h-index is 10 (10 papers with at least 10 citations each). ```python def calculate_h_index(citation_counts): """Calculate h-index from a list of citation counts.""" sorted_counts = sorted(citation_counts, reverse=True) h = 0 for i, count in enumerate(sorted_counts): if count >= i + 1: h = i + 1 else: break return h # Example citations = [120, 80, 55, 40, 22, 18, 15, 12, 10, 8, 5, 3, 2, 2, 1, 1, 0, 0, 0, 0] print(f"h-index: {calculate_h_index(citations)}") # Output: 10 ``` ### Related Author-Level Metrics | Metric | Definition | Advantage | |--------|-----------|-----------| | **h-index** | h papers with >= h citations | Simple, robust to outliers | | **i10-index** | Number of papers with >= 10 citations | Intuitive threshold (Google Scholar uses this) | | **g-index** | Largest g such that top g papers have >= g^2 total citations | Rewards highly cited papers more | | **m-quotient** | h-index divided by years since first publication | Normalizes for career length | | **hI-norm** | h-index divided by average number of co-authors | Adjusts for team size | ```python def calculate_g_index(citation_counts): """Calculate g-index from citation counts.""" sorted_counts = sorted(citation_counts, reverse=True) cumulative = 0 g = 0 for i, count in enumerate(sorted_counts): cumulative += count if cumulative >= (i + 1) ** 2: g = i + 1 return g def calculate_i10_index(citation_counts): """Calculate i10-index.""" return sum(1 for c in citation_counts if c >= 10) print(f"g-index: {calculate_g_index(citations)}") # Output: 19 print(f"i10-index: {calculate_i10_index(citations)}") # Output: 10 ``` ## Journal-Level Metrics ### Journal Impact Factor (JIF) Published annually by Clarivate in the Journal Citation Reports (JCR). The 2-year impact factor for year Y is: ``` JIF(Y) = (Citations in Y to articles published in Y-1 and Y-2) / (Number of citable items published in Y-1 and Y-2) ``` | Metric | Provider | Window | Notable Features | |--------|----------|--------|------------------| | Impact Factor | Clarivate (JCR) | 2-year or 5-year | Gold standard, subscription only | | CiteScore | Scopus (Elsevier) | 4-year | Free, includes all document types | | SJR (Scimago) | Scopus data | 3-year | Weights citations by journal prestige (PageRank-like) | | SNIP | Scopus data | 3-year | Normalizes for citation potential of each field | | h5-index | Google Scholar | 5-year | Free, h-index applied to a journal | ### Looking Up Journal Metrics ```python import requests # Using the OpenAlex API to get journal/source information journal_name = "Nature" response = requests.get( "https://api.openalex.org/sources", params={"filter": f"display_name.search:{journal_name}", "per_page": 5} ) results = response.json()["results"] for source in results: print(f"Name: {source['display_name']}") print(f" ISSN: {source.get('issn_l', 'N/A')}") print(f" Works count: {source.get('works_count', 'N/A')}") print(f" Cited by count: {source.get('cited_by_count', 'N/A')}") print(f" h-index: {source.get('summary_stats', {}).get('h_index', 'N/A')}") print(f" 2-year mean citedness: {source.get('summary_stats', {}).get('2yr_mean_citedness', 'N/A')}") ``` ## Calculating Your Own H-Index ### From Google Scholar Google Scholar profiles automatically display h-index and i10-index. No calculation needed, but coverage is the broadest (includes non-peer-reviewed sources). ### From OpenAlex ```python # OpenAlex provides h-index directly in author profiles author_name = "Geoffrey Hinton" response = requests.get( "https://api.openalex.org/authors", params={"filter": f"display_name.search:{author_name}", "per_page": 1} ) author = response.json()["results"][0] print(f"h-index: {author['summary_stats']['h_index']}") print(f"i10-index: {author['summary_stats']['i10_index']}") print(f"2-year mean citedness: {author['summary_stats']['2yr_mean_citedness']}") ``` ## Responsible Use of Metrics ### Known Limitations 1. **Field dependence**: Average citation rates vary dramatically across disciplines. An h-index of 20 is excellent in mathematics but modest in biomedical sciences. 2. **Career stage bias**: The h-index monotonically increases over time. Always compare within career stage (m-quotient helps). 3. **Self-citation**: Some databases include self-citations in h-index calculation. 4. **Database coverage**: Google Scholar, Scopus, and Web of Science yield different h-index values for the same author. 5. **Gaming**: Metrics can be inflated through citation cartels, salami slicing, and excessive self-citation. ### DORA Declaration The San Francisco Declaration on Research Assessment (DORA) recommends: - Do not use journal-based metrics (such as impact factor) as a surrogate measure of individual research quality. - Assess research on its own merits rather than on the basis of the journal in which it is published. - Use article-level metrics alongside qualitative indicators for assessment. ### Best Practices for Reporting - Always specify the source database and date when reporting h-index - Report multiple metrics rather than relying on a single number - Provide field-normalized indicators (FWCI, SNIP) when comparing across disciplines - Include qualitative achievements alongside quantitative metrics in CVs and promotion cases --- Source attribution: wentorai Original project: https://github.com/wentorai/research-plugins/blob/bf44b3cd617fa94c8a1b254c5d1987142ca3d631/skills/literature/metadata/h-index-guide/SKILL.md License: MIT License information: https://opensource.org/license/mit Original upstream instructions; downloaded from Mega AI Hub. ## Upstream license notice MIT License Copyright (c) 2026 Wentor AI Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. 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