Skip to main content
SpringerLink
Log in

On fractional approach to analysis of linked networks

  • Published:
Scientometrics Aims and scope Submit manuscript

Abstract

In this paper, we present the outer product decomposition of a product of compatible linked networks. It provides a foundation for the fractional approach in network analysis. We discuss the standard and Newman’s normalization of networks. We propose some alternatives for fractional bibliographic coupling measures.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

References

  • Batagelj, V. (2007). WoS2Pajek. Networks from web of science. Version 1.5 (2017). http://vladowiki.fmf.uni-lj.si/doku.php?id=pajek:wos2pajek.

  • Batagelj, V. (2018). Github: biblio—Bibliographic network analysis. https://github.com/bavla/biblio.

  • Batagelj, V., & Cerinšek, M. (2013). On bibliographic networks. Scientometrics, 96(3), 845–864.

    Article  Google Scholar 

  • Batagelj, V., Doreian, P., Ferligoj, A., & Kejžar, N. (2014). Understanding large temporal networks and spatial networks: Exploration, pattern searching, visualization and network evolution. Chichester: Wiley.

    Book  Google Scholar 

  • Carley, K. M. (2003). Dynamic network analysis. In R. Breiger & K. M. Carley (Eds.), Summary of the NRC workshop on social network modeling and analysis (pp. 133–145). Washington, DC: National Research Council.

    Google Scholar 

  • Cerinšek, M., & Batagelj, V. (2015). Network analysis of Zentralblatt MATH data. Scientometrics, 102(1), 977–1001.

    Article  Google Scholar 

  • Cerinšek, M., & Batagelj, V. (2017). Semirings and matrix analysis of networks. In R. Alhajj & J. Rokne (Eds.), Encyclopedia of social network analysis and mining. New York: Springer.

    MATH  Google Scholar 

  • Clarivate Analytics (2018). https://clarivate.com/products/web-of-science/databases/.

  • De Nooy, W., Mrvar, A., & Batagelj, V. (2018). Exploratory social network analysis with Pajek: Revised and expanded edition for updated software., Structural analysis in the social sciences Cambridge: Cambridge University Press.

    Book  Google Scholar 

  • Diesner, J., & Carley, K. M. (2004). Revealing social structure from texts: Meta-matrix text analysis as a novel method for network text analysis, Chapter 4. In V. K. Narayanan & D. J. Armstrong (Eds.), Causal mapping for research in information technology (pp. 81–108). Calgary: Idea Group Inc.

    Google Scholar 

  • Gauffriau, M. (2017). A categorization of arguments for counting methods for publication and citation indicators. Journal of Informetrics, 11(3), 672–684.

    Article  Google Scholar 

  • Kessler, M. (1963). Bibliographic coupling between scientific papers. American Documentation, 14(1), 10–25.

    Article  Google Scholar 

  • Krackhardt, D., & Carley, K. M. (1998). A PCANS model of structure in organization. In Proceedings of the 1998 international symposium on command and control research and technology evidence based research (pp. 113–119), Vienna, VA.

  • Leydesdorff, L., & Park, H. W. (2016). Full and fractional counting in bibliometric networks. Journal of Informetrics, 11(1), 117–120.

    Article  Google Scholar 

  • Lindsey, D. (1980). Production and citation measures in the sociology of science: The problem of multiple authorship. Social Studies of Science, 10(2), 145–162.

    Article  Google Scholar 

  • Marshakova, I. (1973). System of documentation connections based on references (sci). Nauchno-Tekhnicheskaya Informatsiya Seriya, 2(6), 3–8.

    Google Scholar 

  • Newman, M. E. J. (2001). Scientific collaboration networks. II. Shortest paths, weighted networks, and centrality. Physical Review E, 64(1), 016132.

    Article  MathSciNet  Google Scholar 

  • Newman, M. E. J. (2004). Coauthorship networks and patterns of scientific collaboration. In Proceedings of the national academy of sciences of the United States of America (vol. 101, no. Suppl1, pp. 5200–5205).

  • Perianes-Rodriguez, A., Waltman, L., & Van Eck, N. J. (2016). Constructing bibliometric networks: A comparison between full and fractional counting. Journal of Informetrics, 10(4), 1178–1195.

    Article  Google Scholar 

  • Prathap, G., & Mukherjee, S. (2016). A conservation rule for constructing bibliometric network matrices. arXiv:1611.08592

  • Small, H. (1973). Co-citation in the scientific literature: A new measure of the relationship between two documents. Journal of the American Society for Information Science, 24(4), 265–269.

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

The paper is based on presentations on 1274. Sredin seminar, IMFM, Ljubljana, 29. March 2017; NetGloW 2018, St Petersburg, July 4-6, 2018; and COMPSTAT 2018, Iasi, Romania, August 28-31, 2018. This work is supported in part by the Slovenian Research Agency (research program P1-0294 and research projects J1-9187, J7-8279 and BI-US/17-18-045) (Javna Agencija za Raziskovalno Dejavnost RS), project CRoNoS (COST Action IC1408) (European Cooperation in Science and Technology) and by Russian Academic Excellence Project ‘5-100’.

Author information

Authors and Affiliations

  1. Institute of Mathematics, Physics and Mechanics, Jadranska 19, 1000, Ljubljana, Slovenia

    Vladimir Batagelj

  2. University of Primorska, Andrej Marušič Institute, 6000, Koper, Slovenia

    Vladimir Batagelj

  3. National Research University Higher School of Economics, 11 Pokrovsky Boulevard, Moscow, Russia, 101000

    Vladimir Batagelj

Authors
  1. Vladimir Batagelj
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vladimir Batagelj.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Batagelj, V. On fractional approach to analysis of linked networks. Scientometrics 123, 621–633 (2020). https://doi.org/10.1007/s11192-020-03383-y

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11192-020-03383-y

Keywords

Mathematics Subject Classification

JEL Classification

Search

Navigation