Citations: Citations, generally at the end of each article, provide researchers with the list of the prior research relied on for the article. Citations of S&E publications by other S&E publications provide an indication of the impact of publications and of the flow of knowledge or linkage between sectors or geographic locations.

Coauthorship: Coauthorship refers to cases in which there is more than one author listed on a publication. Data on coauthorship can be used to measure collaboration across regions, countries, economies, and institutional sectors. Publication counts of coauthorship use whole counting, resulting in a full count assignment for each country contributing to the article. An article is considered to contain an international coauthorship when there are institutional addresses for authors from two or more different countries. Table SPBS-36 shows international coauthorship from 1996 to 2020.

European Union (EU-27): The European Union (EU) comprises 27 member nations: Austria, Belgium, Bulgaria, Croatia, Cyprus, Czechia, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, the Netherlands, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, and Sweden. Bulgaria and Romania joined the EU in 2007, and Croatia joined in 2013; they are included in the EU grouping for all years analyzed in this report. In 2020, the United Kingdom (UK) left the EU, and the UK is excluded from the EU in the text of the report but is available in the supplemental tables as EU-28.

Fractional counting: Method of counting S&E publications in which credit for coauthored publications is divided among the collaborating institutions or countries based on the proportion of their participating authors. Fractional counting allocates the publication count by the proportion of each of the countries or institutional coauthors named on the article. Fractional counting enables the counts to sum up to the number of total articles. For example, if a paper were authored by two researchers from the University of Oslo, one from the University College London, and one from the University of Washington, half of the paper would be attributed to Norway, and one quarter each to the UK and the United States when the fractions are calculated at the level of researchers. For this report, fractions were calculated at the level of researchers. If an author provides multiple institutions, and those institutions are in different countries, then each country receives an appropriate fraction of the count.

Highly cited articles (HCA): An HCA score is not a perfect measure of influence, but it provides an indication of scientific impact (Waltman, van Eck, and Wouters 2013). The first step is to create a data set of the top 1% most-cited publications in each field and for each year. The HCA score for a country is the share of authors with institutional addresses within that country that have articles among the top 1% of the world’s highly cited articles, relative to all the articles ascribed to that country up to 2018. The HCA score is indexed to 1, so that a country whose authors produce highly cited articles at the expected (i.e., global average) rate has an HCA score of 1.0; that is, 1% of the country’s articles are among the top 1% of the world’s highly cited articles. Countries with authors producing highly cited articles at greater than the expected rate have HCA scores greater than 1, and countries with authors producing influential articles at lower than the expected rate have HCA scores less than 1. For example, assume a world of two countries produced an output of 10,000 articles, with country x authors producing 7,000 articles and country y authors producing 3,000 articles. If both countries had the same influence in the citation records, then country x would have 70 highly cited articles, and country y would have 30 highly cited articles in the top 100 most-cited articles in the world. Each country would have an HCA score of 1. The scores would be different if authors in one of the countries produced a higher proportion of the highly cited articles. For example, if authors in country y produced 50 of the most highly cited articles, then their HCA score would be 1.7, indicating that 1.7% of the articles of country y’s authors (50 out of 3,000) are among the top 1% of the world’s highly cited articles. For country x, the HCA score would be 0.7 (50 out of 7,000).

International collaboration index: The international collaboration index is calculated as follows: ICxy = (Cxy / Cx) / (Cy / Cw), where ICxy is the index of collaboration between country x and country y, Cxy is the number of papers coauthored between country x and country y, Cx is the total number of international coauthorships by country x, Cy is the total number of international coauthorships by country y, and Cw is the total number of international coauthorships in the database. An index greater than 1.0 means that a country-country pair has a stronger-than-expected tendency to collaborate; an index less than 1.0 indicates a weaker-than-expected tendency to collaborate (Table SPBS-39).

Relative citation: The relative citation is a normalization of the relative scientific impact of papers produced by a given country that takes into consideration the fact that citation behavior varies between fields and years of publication. For a paper in a given scientific field and publication year, the citation count is then divided by the average count of all papers in the relevant field and publication year.

Relative citation index: The relative citation index normalizes cross-national citation data for variations in relative size of publication output. It is computed by dividing the share of the citing country’s outgoing citations going to the cited country and then dividing this by the share of publications attributed to the cited country.

Whole counting: This measure (also called full or integer counting) assigns one count to each country or institutional sector involved in coauthoring the article, irrespective of its proportionate involvement in authorship. Whereas fractional counting aims to assess the proportionate contributions of countries or sectors, whole counting aims instead to assess the participation of countries or sectors. One result of this difference is that the sum of articles from countries or institutional sectors will exceed the total number of articles when whole counting is used. For the United States in 2018, there were 435,000 publications in the Scopus database as measured on a fractional count basis and 563,000 as measured on a whole count basis (Table SPBS-2 and Table SPBS-17). In the full-counting method, each paper is counted once for each entity listed in the address field. For example, if a paper was authored by two researchers from the University of Oslo, one from the University College London, and one from the University of Washington, the paper would be counted once for Norway, once for the UK, and once for the United States. When it comes to aggregating groups of institutions (e.g., research consortia) or groups of countries (e.g., the EU), double counting is avoided. This means that if authors from Croatia and France co-published a paper, this paper would be credited only once when counting papers for the EU, even though each country had been credited with one publication count.

Key to Acronyms and Abbreviations

CORD-19: COVID-19 Open Research Dataset

EU: European Union

HCA: highly cited articles

IDR: interdisciplinary research

MDR: multidisciplinary research

NASEM: National Academy of Sciences, Engineering, and Medicine

NRC: National Research Council

NSF: National Science Foundation

OSTP: Office of Science and Technology Policy

R&D: research and development

RCI: relative citation index

RCUK: Research Councils of the United Kingdom

S&E: science and engineering

SDR: NCSES Survey of Doctorate Recipients

TOD: Taxonomy of Disciplines

UK: United Kingdom

WoS: Web of Science