Source-linked AI summary
Constructing bibliometric networks: A comparison between full and fractional counting
Antonio Perianes-Rodriguez, Ludo Waltman, Nees Jan van Eck
TL;DR
Bibliometric network construction has received less attention than network analysis, despite different counting approaches being possible. The paper defines and compares full and fractional counting across network types and empirical examples, finding that the methods can yield very different results and that fractional counting is preferable for many purposes.
Problem
Bibliometric network analysis is well established, but the construction of these networks has received remarkably little attention.
Method
The paper defines full and fractional counting for co-authorship, bibliographic coupling, and co-citation networks and compares them in two empirical examples.
Results
The full and fractional counting methods yield very different results in analyses of university co-authorship and journal bibliographic coupling networks.
Takeaways & Limitations
For many purposes, the paper concludes that fractional counting is preferable to full counting.
Takeaways & Limitations
The paper notes a disadvantage of fractional counting that may not be desirable.
Abstract
from arXiv · showhide
The analysis of bibliometric networks, such as co-authorship, bibliographic coupling, and co-citation networks, has received a considerable amount of attention. Much less attention has been paid to the construction of these networks. We point out that different approaches can be taken to construct a bibliometric network. Normally the full counting approach is used, but we propose an alternative fractional counting approach. The basic idea of the fractional counting approach is that each action, such as co-authoring or citing a publication, should have equal weight, regardless of for instance the number of authors, citations, or references of a publication. We present two empirical analyses in which the full and fractional counting approaches yield very different results. These analyses deal with co-authorship networks of universities and bibliographic coupling networks of journals. Based on theoretical considerations and on the empirical analyses, we conclude that for many purposes the fractional counting approach is preferable over the full counting one.
1. Introduction
Constructing bibliometric networks has received little attention despite allowing different counting approaches. This paper distinguishes full and fractional counting, demonstrates that they can produce very different results, and argues that fractional counting is often preferable.
- Motivation: Bibliometric network construction is often treated as trivial, but the paper argues that it requires special consideration.
- Contribution: The paper distinguishes full and fractional counting as alternative approaches to constructing bibliometric networks.
- Counting approaches: For a researcher with five co-authors, full counting gives five co-authorship links weight 1, while fractional counting gives each link weight 1 / 5 and total weight 1.
- Scope: The study examines co-authorship, bibliographic coupling, and co-citation networks, while noting that the ideas extend to other bibliometric networks.
- Empirical comparison: Two examples—university co-authorship networks and journal bibliographic coupling networks—show large differences between the methods, with fractional counting judged preferable.
- Implementation: Both counting methods are available in VOSviewer, which supports analyses using data from bibliographic databases such as Web of Science and Scopus.
2. Constructing bibliometric networks
The paper distinguishes full and fractional counting as alternative methods for constructing bibliometric networks. Fractional counting assigns link weights so each action has overall weight one, and the authors argue it is preferable for many purposes.
- The paper examines full and fractional counting for co-authorship, bibliographic coupling, and co-citation networks, while emphasizing that the approach also applies to other bibliometric networks.
- Full counting vs. fractional counting: Full counting gives every link from an action weight one, so an action's total weight equals the number of resulting links.
- Full counting vs. fractional counting: Fractional counting gives each link a fractional weight so the total weight of an action equals one.
- Arguments in favor of fractional counting: In bibliographic coupling, full counting gives highly cited references more influence, whereas fractional counting treats each cited reference as equally representative of a publication's topic.The authors note that a closely related, lowly cited article may be more representative than a broadly focused, highly cited review.
- Conclusion: The authors conclude that fractional counting is preferable to full counting for many purposes based on theoretical considerations and empirical analyses.
- Co-authorship networks: In the empirical co-authorship example, each researcher's total fractional link weight equals the number of publications authored, a general property of the approach.
3. Empirical analysis
The empirical analyses compare full and fractional counting in university co-authorship and journal bibliographic-coupling networks. The methods can produce substantially different network structures and rankings, largely because full counting gives disproportionate influence to a small number of highly collaborative publications.
- Scope: The study compares full and fractional counting in co-authorship networks of universities and bibliographic-coupling networks of journals.These analyses were selected because the two counting methods yield very different results.
- Co-authorship networks: Fractional-counting visualizations show clearer country-based university groupings, whereas full-counting visualizations suggest that national borders play only a minor role.The two networks use the same underlying data but give very different impressions of worldwide scientific collaboration.
- Co-authorship networks: Full counting allows a very small number of publications with many co-authoring universities to have a huge effect on co-authorship networks.Publications involving more than 100 universities account for almost 50% of all co-authorship links, despite numbering only 158.
- Co-authorship networks: 0.05% of publications account for 62% of co-authorship links under full counting, but the same publications account for only 4.0% under fractional counting.The contrast shows how fractional counting reduces the influence of publications with many co-authors.
- Bibliographic coupling networks: For ACSE and Scientometrics, four citations generate the strong full-counting relationship, while fractional counting assigns the relationship a much lower overall weight.The first two publications account for 99.9% of all full-counting coupling links between the journals.
4. Discussion and conclusion
The paper argues that bibliometric-network construction deserves more attention because full and fractional counting can produce substantially different results. Across two empirical examples, fractional counting is often more useful, although its interpretation is more difficult and the preferred perspective depends on the analysis purpose.
- Motivation: Construction choices have received little attention despite being a prerequisite for analyzing and visualizing bibliometric networks.The paper challenges the implicit assumption that full counting is the only construction method.
- Contribution: The authors emphasize that different construction approaches can yield very different bibliometric-network results.They specifically frame the choice between full and fractional counting as consequential for network analysis.
- Counting principles: Fractional counting gives each co-authoring or citing action equal weight, whereas full counting can assign much greater weight to some actions.The authors state that unequal action weights may be undesirable.
- Empirical findings: Full and fractional counting make a big difference in practice, especially in the university co-authorship and journal bibliographic-coupling examples.The paper reports strong effects on both network types, while differences may be limited in some cases.
- Empirical findings: In university co-authorship networks, full counting makes a few large-university publications dominant, whereas fractional counting strongly reduces their influence.The resulting visualizations differ in whether scientific collaboration appears organized mainly across or within national borders.
- Empirical findings: In journal bibliographic coupling, full counting can make a few highly cited publications dominate relationships, while fractional counting gives those citations much less influence.For example, Scientometrics appears much less related to the cited journals under fractional counting.
- Conclusion and limitations: The more useful counting perspective depends on the underlying data and the purpose of the analysis, and alternative fractionalization schemes remain possible.The paper leaves several possible fractionalization choices for future research.
- Conclusion and limitations: Fractional counting is preferable in many situations, but it is harder to explain because it produces non-integer link weights.The authors also note that fractional bibliographic-coupling link weights may decrease over time as cited publications receive additional citations.
Appendix
The appendix explains the authors’ fractional co-authorship counting method and contrasts it with related approaches. Its key design choice is a denominator of n_k − 1, which makes each co-authoring action have the same total weight.
- Authors’ method: The authors’ fractional method assigns each co-authorship link a weight of 1 / (n_k − 1), unlike full counting’s unit links.The denominator is chosen so that a researcher’s co-authoring action does not depend on the number of collaborators.
- Comparison of denominators: Using n_k rather than n_k − 1 gives different actions different total weights, only approximately equalizing them.With n_k = 4, three links total 0.75; with n_k = 10, nine links total 0.9.
- Comparison of denominators: With denominator n_k − 1, both three- and nine-collaborator examples produce a total co-authorship weight of 1.The examples are 3 × (1 / 3) = 1 and 9 × (1 / 9) = 1.
- Related approaches: The third approach of Batagelj and Cerinšek fractionalizes by total publication-level co-authorship links, whereas the authors’ method fractionalizes by links associated with one co-author.Links calculated with the third approach therefore have lower weights than those calculated with the first two approaches.
- Interpretation: From an individual researcher’s perspective, co-authoring with a small number of other researchers receives more weight than co-authoring with many others.The appendix illustrates differences among approaches using co-authorship matrices and compares them with full counting.