Skip to main content

Growth patterns of the network of international collaboration in science


International knowledge flows might be eroding national borders of innovation systems and contributing for the emergence of an international system of innovation. This paper investigates how far the scientific international collaboration has developed and how stable the structure of those collaborations is, evaluating the properties of those networks and their long term behaviour. The data collected and analyzed show that international collaboration has been growing with a peculiar pattern—faster than an exponential growth-, shaping a scale-free network that has preserved its structure while it grows. This paper analyses the properties of this network and the implications of those properties for an emerging global innovation system in terms of growth, hierarchy, opportunity, challenges, and robustness and for the generation and transfer of technology

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3


  1. WebOfScience has 252 different S&E disciplines. To process those data by more aggregated areas we applied Braun et al. (1995a, b) suggestion - as close as possible: 170 S&E disciplines were aggregated into 27 fields. In this aggregation 82 S&E disciplines were not used, since they are related to human and social sciences and have no correspondence in the aggregation strategy of Braun et al. (1995a, b).

  2. We do as Wagner and Leydesdorff (2005) that uses all types of documents in their analysis.

  3. Barabási describes this moment (2016, chapter 0, personal introduction): "Could the WWW be still broken into many disconnected components? Or is it already one big network, as everyone perceived it back then? These were intriguing questions, no matter the outcome. To answer it we needed the Web’s degree distribution, which was now provided by Hawoong's robot. The data granted us our first real surprise: We did not see the Poisson distribution that random network theory predicted. A power law greeted us instead".

  4. A very didactic explanation of the relationship between of phenomena following a power law and the scale-free nature of networks can be found in Barabási (2016, Sect. 4.2).

  5. The prominent position of the USA and China in 2015 is related both with their size but also with the level of formation of their scientific institutions. If we look to the data for 2000, China was only in the eighth position—a previous stage of their then growing scientific infrastructure.

  6. In this analysis the country of the paper is attributed to the address of the first author.

  7. The relationship between income and the formation of national systems of innovation is discussed in a previous paper (Ribeiro et al. 2006).

  8. Exceptions: Qatar and very small European countries—Andorra, Liechtenstein, Monaco, San Marino.

  9. In the collaboration network the links represent the scientific co-authorship between two institutions for each article indexed in the ISI database. Then, if two institutions have published in collaboration, for example, one hundred articles, it will be generated also one hundred links between the nodes that represent those two institutions. Therefore, the quantity of links among the institutions in the network represents the intensity of the collaboration among those institutions.

  10. Wagner et al .(2015, p. 6) analyze data from 1990 to 2011, and find a growth in the "number of coauthor relationships (links)" that is "disproportionately large compared to the growth in the number of addresses".

  11. A comparison with patent citation of ISI-indexed paper as a knowledge flow for firms and co-authorship of scientific papers: in 2009, the leading firm in patents with citation of ISI-indexed paper was Microsoft, with 333 patents - or links (Ribeiro et al. 2014, Table 2, p. 72). Microsoft has more than 650 connections (links) through international co-authorship. The leading firm in connections through international co-authorship in our preliminary calculations is Novartis, with more than 5000 links.

  12. It could be intriguing to observe that our power law exponents are smaller than 2. This power law exponents corresponds to Baribási’s degrees of distribution exponents—see Barabási (2016, Image 4.2). Barabási (2016, Sect. 4.7) asks why we do not see networks with degree exponents smaller than 2. Our degrees exponents in Table 5 are smaller than 2 because our network in multi-link (our nodes, institutions, may have more links than one, but Barabási’s nodes have only one link).

  13. The total of network links in Table 6 is greater than the sum of collaboration RI-Firm and Firm-Firm in Table 2 because for the distribution of connectivity analysis in Table 6 the nodes (papers) that show at least one Firm as author are selected and, then, all their connections are analyzed—regardless if the connection originates from one of their Firm or RI author. This criteria is broader than the selection of connections of the type RI-Firm or Firm-Firm (Table 2) because in the former criteria also will be considered connections that originate from the other RI authors of the paper that shows Firm among theirs author and achieve RI authors of others countries papers—being a RI-RI connection. In the distribution of connectivity analysis of Table 6 we are just selecting from the Table 5 the subset of nodes that involves firms and comparing their global behavior (exponents) to see if there is a more homogenous distribution (lower exponent), i.e., lower hierarchy, or a more heterogeneous distribution (higher exponent), i.e., higher hierarchy when the firms nodes behavior is compared to the whole network behavior.


  • Adams, J. (2013). The fourth age of research. Nature, 497, 557–559.

    Article  Google Scholar 

  • Barabási, A.-L. (2016) Network Science. Cambridge: Cambridge University Press (available at

  • Barabási, A.-L., & Albert, R. (1999). Emergence of scaling in random networks. Science, 285, 509–512.

    MathSciNet  MATH  Google Scholar 

  • Barabási, A.-L., Jeong, H., Néda, Z., Ravasz, E., Schubert, A., & Vicsek, T. (2002). Evolution of the social network of scientific collaborations. Physica A, 311, 590–614.

    MathSciNet  Article  MATH  Google Scholar 

  • Braun, T., Glanzel, W., & Grupp, H. (1995a). The Weight of 50 Nations in 27 Science Areas, 1989–1993 (Part I: All fields combined, Mathematics, Engineering, Chemistry and Physics). Scientometrics, 33(3), 263–293.

    Article  Google Scholar 

  • Braun, T., Glanzel, W., & Grupp, H. (1995b). The Weight of 50 Nations in 27 Science Areas, 1989–1993 (Part II: Life Sciences). Scientometrics, 34(2), 207–237.

    Article  Google Scholar 

  • Britto, G., Camargo, O. S., Kruss, G., & Albuquerque, E. M. (2013). Global interactions between firms and universities: global innovation networks as first steps towards a Global Innovation System. Innovation and Development, 3(1), 71–88.

    Article  Google Scholar 

  • Dunning, J., & Lundan, S. (2008). Multinational enterprises and the global economy (2nd ed.). Cheltenham: Edward Elgar.

    Google Scholar 

  • Freeman, R. (2010). Globalization of scientific and engineering talent: international mobility of students, workers, and ideas and the world economy. Economics of Innovation and New Technology, 19(5), 393–406.

    Article  Google Scholar 

  • Freeman, R. (2017). Migration of ideas. Science, 356(6339), 696–697.

    Article  Google Scholar 

  • Freeman, R., Gangulli, I., & Murciano-Goroff, R. (2015). Why and wherefore of increased scientific collaboration. In A. Jaffe & B. Jones (Eds.), The changing frontier: Rethinking science and innovation policy (pp. 17–48). Chicago: NBER/University of Chicago Press.

    Google Scholar 

  • Gilden D. L., Thornton T, & Mallon M. W. (1995) Science, Vol. 267, p. 1837–1839.

  • Glänzel, W., & Schubert, A. (2005). Domesticity and internationality in co-authorship, references and citations. Scientometrics, 65(3), 323–342.

    Article  Google Scholar 

  • Gontis, V., Kaulakys, B., Alaburda, M., & Ruseckas, J. (2004). Evolution of complex systems and 1/f noise: From physics to financial markets. Solid State Phenomena, 97–98, 65–70.

    Article  Google Scholar 

  • Jones, B. F. (2011). As science evolves, how can science policy? In J. Lerner & S. Stern (Eds.), Innovation policy and the economy (Vol. 11, pp. 103–131). Chicago: University of Chicago Press.

    Google Scholar 

  • Katz, J., & Martin, B. (1997). What is research collaboration? Research Policy, 26(1), 1–18.

    Article  Google Scholar 

  • Kaulakys, B., & Meökauskas, T. (1998). Modeling 1/f noise. Physical Review E, 58, 7013–7019.

    Article  Google Scholar 

  • Kruss, G., Lee, K., Suzigan, W., Albuquerque, E. (2015). Introduction. In: Albuquerque, E., Suzigan, W., Kruss, G., Lee, K. (Eds) Developing National Systems of Innovation. University-Industry interactions in the Global South. Cheltenham/Ottawa: Edward Elgar/IDRC, pp. 1–28 (available at

  • Maxim, V., Xendur, Levent, Fadili, Jalal, Suckling, John, Gould, Rebecca, Howard, Rob, et al. (2005). Fractional Gaussian noise, functional MRI and Alzheimer’s disease. NeuroImage, 25, 141–158.

    Article  Google Scholar 

  • National Science Board. (1996). Science and engineering indicators 1996. Arlington: National Science Foundation.

    Google Scholar 

  • National Science Board. (2016). Science and engineering indicators 2016. Arlington: National Science Foundation.

    Google Scholar 

  • NATURE (2016) International research collaborations on the rise. Nature Index (—accessed 19 november 2016).

  • Nelson, R., & Rosenberg, N. (1995). Introduction. In R. Nelson (Ed.), National innovation systems: A comparative analysis. New York, Oxford: Oxford University.

    Google Scholar 

  • OECD. (2015). OECD Science, Technology and Industry Scoreboard 2015: Innovation for growth and society. Paris: OECD Publishing.

    Book  Google Scholar 

  • OECD and SCImago Research Group (CSIC) (2016) Compendium of Bibliometric Science Indicators. OECD, Paris. Accessed from

  • Patel, P., & Pavitt, K. (1998). National systems of innovation under strain: The internationalization of corporate R&D. Brighton: SPRU.

    Google Scholar 

  • Ribeiro, L. C., Kruss, G., Britto, G., Ruiz, R. M., Bernardes, A. T., & Albuquerque, E. M. (2014). A methodology for unveiling global innovation networks: Patent citations as clues to cross border knowledge flows. Scientometrics, 101, 61–83.

    Article  Google Scholar 

  • Ribeiro, L. C., Ruiz, R. M., Bernardes, A. T., & Albuquerque, E. M. (2006). Science in the developing world: Running twice as fast? Computer Science & Engineering: An International Journal, 8, 86–92.

    Article  Google Scholar 

  • Science. (2017). Crossing borders along an endless frontier. Science, 356(6339), 694–697.

    Google Scholar 

  • Soete, L., Verspagen, B., & Weel, B. (2010). Systems of innovation. In B. Hall & N. Rosenberg (Eds.), Handbook of the economics of innovation (Vol. II). Amsterdam: North Holland.

    Google Scholar 

  • Wagner, C., & Leydesdorff, L. (2005). Network structure, self-organization, and the growth of international collaboration in science. Research Policy, 34(10), 1608–1618.

    Article  Google Scholar 

  • Wagner, C., Park, H. W., Leydesdorff, L. (2015) The continuing growth of global cooperation networks in research: A conundrum for national governments. PLOS one, July 21, 2015

  • Wong, H. (2003). Low-frequency noise study in electron devices: Review and update. Microelectronics Reliability, 43, 585–599.

    Article  Google Scholar 

  • Yamamoto, Y., Nakamura, Y., Sato, H., Yamamoto, M., Kato, K., & Hughson, R. (1995). On the fractal nature of heart rate variability in humans: Effects of vagal blockade. American Physiological Society, R830, 0363–6119.

    Google Scholar 

Download references


We thank the financial support from CNPq (Processes 459627/2014-7, 302857/2015-0 and 401054/2016-0). We thank Giulia Tonon and José Carlos Miranda for research assistance. Comments, criticisms and suggestions from two anonimous referees from Scientometrics helped to improve our earlier version of this paper. The usual disclaimer holds.

Author information

Authors and Affiliations


Corresponding author

Correspondence to Eduardo Motta Albuquerque.



Document type Articles
Article 5.688.001
Meeting abstract 1.113.336
Proceedings paper 1.107.212
Editorial material 439.781
Book review 410.670
Article; proceedings paper 400.577
Review 311.397
Letter 232.354
News item 127.357
Correction 61.917
Poetry 31.037
Biographical-item 30.376
Art exhibit review 14.230
Film review 9.707
Record review 8.676
Review; book chapter 7.614
Fiction, creative prose 4.440
Article; book chapter 4.158
Theater review 2.995
Dance performance review 2.886
Reprint 2.756
Bibliography 1.889
Music score review 1.887
TV review, radio review 1.788
Music performance review 1.737
Software review 1.386
Excerpt 586
Editorial material; book chapt 522
Script 241
Database review 183
Music score 92
Hardware review 63
Biographical-item; book chapter 16
Meeting summary 8
Correction; book chapter 7
Letter; Book chapter 5
Main cite 5
Chronology 5
Reprint; book chapter 4
Review; book 3
Abstract of published item 3
Main cite; book chapter 2
Article; book 2
Book 1
  1. Source: WebOfScience, authors’ elaboration

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Ribeiro, L.C., Rapini, M.S., Silva, L.A. et al. Growth patterns of the network of international collaboration in science. Scientometrics 114, 159–179 (2018).

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI:


  • Knowledge flows
  • International co-authorships
  • Science
  • Innovation systems