, Volume 121, Issue 2, pp 1045–1065 | Cite as

Cooperation, scale-invariance and complex innovation systems: a generalization

  • J. Sylvan Katz
  • Guillermo Armando Ronda-PupoEmail author


The focus of this paper is the question “Can scale-invariant properties of collaborative research activities of a complex innovation system be quantified, modeled and used to inform decision makers about the effect that cooperation has on the impact of published peer-reviewed research?” Over the past few decades cooperative research activities have been extensively studied. Presently, encouragement and support for collaborative research and training is a cornerstone of many innovation policies and programs. Concurrently, the study of complex systems has produced tools and techniques that can be applied to the study of innovation systems. They have been shown to be complex systems with scale-invariant properties that can be measured and modeled providing novel insights to decision makers. An important factor contributing to the emergence of scale-invariant properties is the inseparable tension between competitive and cooperative activities among actors within a complex system. Peer-reviewed papers index in the 1990–2010 Web of Science and citations to these papers are used as a partial measure of size and impact, respectively. Documents are classified into 14 natural, health and applied sciences fields. Numbers of authors and country information from each paper are used to classify documents into various types of cooperation. Scale-invariant correlations between impact and sizes where prepared to provide measures and models used to explore the effects of cooperation types. It is shown that collaborative research tends to have greater impact and for a longer period of time that non-collaborative research. Cooperation in the more applied fields show higher growth of impact when compared to the growth of their sizes than cooperation in fields closer to the basic or ‘blue sky’ end of the R&D spectrum. Cooperation in a complex innovation system can have significant effects on the relative growth of impact with respect to growth of size and it enhances the sustainability of the Matthew Effect over time. Cooperative activities appear to sustain self-organization in a complex innovation system.


Allometric Cooperation Collaboration Complex system Innovation Power-law Scale-invariant Self-similar Scale independent 

JEL Classification




This work was supported, in part, by FONDECYT Chile. Grant # 1180200.


  1. Archambault, É., Beauchesne, O. H., & Caruso, J. (2014a). Towards a multilingual, comprehensive and open scientific journal ontology. Available at, Accessed 25 Aug 2019.
  2. Archambault, É., Beauchesne, O. H., Côté, G., & Roberge, G. (2011). Scale-adjusted metrics of scientific collaboration. Paper presented at the 13th international conference of the International Society for Scientometrics and Informetrics Durban, South Africa.Google Scholar
  3. Archambault, É., Beauchesne, O. H., Côté, G., & Roberge, G. (2014b). Scale-adjusted metrics of scientific collaboration. Retrieved from, Accessed 25 Aug 2019.
  4. Avkiran, N. K. (1997). Scientific collaboration in finance does not lead to better quality research. Scientometrics, 39(2), 173–184. Scholar
  5. Barabási, A. L. (2014). Network scienceChapter 5 The Barabási-Albert Model. This book is licensed under a Creative Commons: CC BY-NC-SA 2.0. Available at Accessed 25 Aug 2019.
  6. Barabási, A. L., & Albert, R. (1999). Emergence of scaling in random networks. Science, 286, 509–512. Scholar
  7. Barabási, A. L., Jeong, H., Néda, Z., Ravasz, E., Schubert, A., & Vicsek, T. (2002). Evolution of the social network of scientific collaborations. Physica A: Statistical Mechanics and its Applications, 311(3–4), 590–614. Scholar
  8. Barabasi, A. L., & Reka, A. (1999). Emergence of scaling in random networks. Science, 286(5439), 509–512. Scholar
  9. Baranger, M. (2001). Chaos, complexity, and entropy: A physics talk for non-physicists. Wesleyan University Physics Dept. Colloquium. Retrieved from Accessed 25 Aug 2019.
  10. Bar-Yam, Y. (2001). Introducing complex systems. Boston, MA: NECSI Press.Google Scholar
  11. Beaver, D. D. (2001). Reflections on scientific collaboration, (and its study): Past, present, and future. Scientometrics, 52(3), 365–377. Scholar
  12. Bettencourt, L. M. A., Lobo, J., Strumsky, D., & West, G. (2010). Urban scaling and its deviations: Revealing the structure of wealth, innovation and crime across cities. PLoS ONE, 5(11), e13541. Scholar
  13. Biggiero, L., & Angelini, P. P. (2015). Hunting scale-free properties in collaboration networks: Self-organization, power-law and policy issues in the European aerospace research area. Technological Forecasting and Social Change, 94, 21–43. Scholar
  14. Coccia, M., & Bozeman, B. (2016). Allometric models to measure and analyze the evolution of international research collaboration. Scientometrics, 108, 1065–1084. Scholar
  15. Elena Luna-Morales, M. (2012). International scientific collaboration and recognition of Mexican science from 1980 to 2004. Investigación Bibliotecológica, 26(57), 103–129.CrossRefGoogle Scholar
  16. Frame, J. D., & Carpenter, M. P. (1979). International research collaboration. Social Studies of Science, 4, 481–497. Scholar
  17. Gibrat, R. (1931). Les Inégalités économiques. Paris.Google Scholar
  18. Girvan, M., & Newman, M. E. J. (2002). Community structure in social and biological networks. Proceedings of the National Academy of Sciences of the United States of America, 99(12), 7821–7826. Scholar
  19. Glänzel, W. (2002). Co-authorship patterns and trends in the sciences (1980–1998): A bibliometric study with implications for database indexing and search strategies. Library Trends, 50(3), 461–473.Google Scholar
  20. González-Teruel, A., González-Alcaide, G., Barrios, M., & Abad-García, M.-F. (2015). Mapping recent information behavior research: An analysis of co-authorship and co-citation networks. Scientometrics, 103(2), 687–705. Scholar
  21. Hara, N., Solomon, P., Kim, S. L., & Sonnenwald, D. H. (2003). An emerging view of scientific collaboration: Scientists’ perspectives on collaboration and factors that impact collaboration. Journal of the American Society for Information Science and Technology, 54(10), 952–965. Scholar
  22. He, J.-H., & Liu, Jun-Fang. (2009). Allometric scaling laws in biology and physics. Chaos, Solitons & Fractals, 41(4), 1836–1838. Scholar
  23. Hébert-Dufresne, L., Allard, A., Young, J.-G., & Dubé, L. J. (2016). Constrained growth of complex scale-independent systems. Physical Review E, 93(3), 032304. Scholar
  24. Hébert-Dufresne, L., Laurence, E., Allard, A., Young, J.-G., & Dubé, L. J. (2015). Complex networks as an emerging property of hierarchical preferential attachment. Physical Review E, 92(6), 062809. Scholar
  25. Hicks, D., & Katz, J. S. (1996). Science policy for a highly collaborative science system. Science and Public Policy, 23(1), 39–44. Scholar
  26. Katz, J. S. (1994). Geographical proximity and scientific collaboration. Scientometrics, 31(1), 31–43. Scholar
  27. Katz, J. S. (2000). Scale-independent indicators and research assessment. Science and Public Policy, 27(1), 23–36.CrossRefGoogle Scholar
  28. Katz, J. S. (2005). Scale-independent bibliometric indicators. Measurement: Interdisciplinary Research and Perspectives, 3(1), 24–28.Google Scholar
  29. Katz, J. S. (2006). Indicators for complex innovation systems. Research Policy, 35, 893–909.CrossRefGoogle Scholar
  30. Katz, J. S. (2012). Scale-independent measures: Theory and practice. Paper presented at the 17th international conference on science and technology indicators, September 5–8, Montreal, Canada.
  31. Katz, J. S. (2016a). Policy considerations for evidence-based measures of complex innovation systems. Paper presented at the transforming innovation—50th anniversary conference, SPRU, University of Sussex, September 7–9, 2016.Google Scholar
  32. Katz, J. S. (2016b). What is a complex innovation system? PLoS ONE, 11(6), e0156150. Scholar
  33. Katz, J. S., & Cothey, V. (2006). Web indicators for complex innovation systems. Research Evaluation, 14(2), 85–95.CrossRefGoogle Scholar
  34. Katz, J. S., & Hicks, D. (1997). How much is a collaboration worth? A calibrated bibliometric model. Scientometrics, 40(3), 541–554. Scholar
  35. Katz, J. S., & Martin, B. R. (1997). What is research collaboration? Research Policy, 26(1), 1–18. Scholar
  36. Kliegl, R., & Bates, D. (2010). International collaboration in psychology is on the rise. Scientometrics, 87(1), 149–158. Scholar
  37. Kuhn, T., Perc, M., & Helbing, D. (2014). inheritance patterns in citation networks reveal scientific memes. Physical Review X. Scholar
  38. Luukkonen, T., Tijssen, R. J. W., Persson, O., & Sivertsen, G. (1993). The measure of international scientific collaboration. Scientometrics, 28(1), 15–36. Scholar
  39. Merton, R. K. (1968). The Matthew effect in science. Science, 159(3810), 56–63.CrossRefGoogle Scholar
  40. Merton, R. K. (1988). The Matthew effect in science, II: Cumulative advantage and the symbolism of intellectual property. ISIS, 79, 606–623.CrossRefGoogle Scholar
  41. Milojević, S. (2010). Modes of collaboration in modern science: Beyond power laws and preferential attachment. Journal of the American Society for Information Science and Technology, 61(7), 1410–1423. Scholar
  42. Newman, M. E. J. (2001a). Scientific collaboration networks. I. Network construction and fundamental results. Physical Review E, 64, 016131.CrossRefGoogle Scholar
  43. Newman, M. E. J. (2001b). The structure of scientific collaboration networks. Proceedings of the National Academy of Sciences, 98(2), 404–409. Scholar
  44. Newman, M. E. J. (2004). Coauthorship networks and patterns of scientific collaboration. PNAS, 101(supplement 1), 5200–5205.CrossRefGoogle Scholar
  45. Newman, M. E. J. (2005). Power laws, Pareto distributions and Zipf’s law. Contemporary Physics, 46(5), 323–351.CrossRefGoogle Scholar
  46. Newman, M. E. J. (2011). SIGMETRICS posting. Accessed 25 Aug 2019.
  47. Palla, G., Derenyi, I., Farkas, I., & Vicsek, T. (2005). Uncovering the overlapping community structure of complex networks in nature and society. Nature, 435, 814–818.CrossRefGoogle Scholar
  48. Pan, R. K., Kaski, K., & Fortunato, S. (2012). World citation and collaboration networks: Uncovering the role of geography in science. arXiv preprint, arXiv:1209.0781.
  49. Perc, M. (2013). Self-organization of progress across the century of physics. Scientific Reports. Scholar
  50. Perc, M. (2014). The Matthew effect in empirical data. Journal of the Royal Society, Interface, 11(98), 20140378. Scholar
  51. Perc, M., Jordan, J. J., Rand, D. G., Wang, Z., Boccaletti, S., & Szolnoki, A. (2017). Statistical physics of human cooperation. Physics Reports, 687, 1–51. Scholar
  52. Persson, O., Glänzel, W., & Danell, R. (2004). Inflationary bibliometric values: The role of scientific collaboration and the need for relative indicators in evaluative studies. Scientometrics, 60(3), 421–432. Scholar
  53. Ronda-Pupo, G. A., & Katz, J. S. (2016a). The power-law relationship between citation-based performance and collaboration in articles in management journals: A scale-independent approach. Journal of the Association for Information Science and Technology, 67(10), 2565–2572. Scholar
  54. Ronda-Pupo, G. A., & Katz, J. S. (2016b). The scaling relationship between citation-based performance and co-authorship patterns in natural sciences. Journal of the Association for Information Science and Technology, 68(5), 1257–1265. Scholar
  55. Rousseau, R. (2000). Are multi-authored articles cited more than single-authored ones? Are collaborations with authors from other countries more cited than collaborations within the country? A case study. Paper presented at the Collaboration in Science and in Technology, Berlin.Google Scholar
  56. Rousseau, R., & Ding, J. (2015). Does international collaboration yield a higher citation potential for US scientists publishing in highly visible interdisciplinary Journals? Journal of the Association for Information Science and Technology, 67(4), 1009–1013. Scholar
  57. Rus, C. O. (2008). Fibonacci numbers in horticulture. Bulletin of University of Agricultural Sciences and Veterinary Medicine Cluj-Napoca. Horticulture, 65(2), 603–607.Google Scholar
  58. Sahal, D. (1981). Patterns of technological innovation. New York: Addison-Wesley.Google Scholar
  59. Smith, J. (2009). Use and misuse of the reduced major axis for line-fitting. American Journal of Physical Anthropology, 140, 476–484.CrossRefGoogle Scholar
  60. Stokols, D., Hall, K. L., Taylor, B. K., & Moser, R. P. (2008). The science of team science—Overview of the field and introduction to the supplement. American Journal of Preventive Medicine, 35(2), S77–S89. Scholar
  61. Tang, L., & Shapira, P. (2010). Regional development and interregional collaboration in the growth of nanotechnology research in China. Scientometrics, 86(2), 299–315. Scholar
  62. van Raan, A. F. J. (1990). Fractal dimension of co-citations. Nature, 347(6294), 626. Scholar
  63. van Raan, A. F. J. (1998). The influence of international collaboration on the impact of research results. Scientometrics, 42(3), 423–428. Scholar
  64. van Raan, A. F. J. (2013). Universities scale like cities. PLoS ONE, 8(3), e59384. Scholar
  65. Wagner, C. S., & Leydesdorff, L. (2005). Network structure, self-organization, and the growth of international collaboration in science. Research Policy, 34(10), 1608–1618. Scholar
  66. Wang, X.-X., Liu, H.-M., & Yang, C.-X. (2013). Why complex organizations cooperate with competitors? An systematic perspective. Journal of Applied Sciences, 13(20), 4293–4299. Scholar
  67. Warton, D. I., Wright, I. J., Falster, D. S., & Westoby, M. (2006). Bivariate line-fitting methods for allometry. Biological Reviews, 81(02), 259–291.CrossRefGoogle Scholar
  68. West, G. B., Brown, J. H., & Enquist, B. J. (1997). A general model for the origin of allometric scaling laws in biology. Science, 276(5309), 122–126. Scholar
  69. Zhai, L., Yan, X., Shibchurn, J., & Song, X. (2014). Evolutionary analysis of international collaboration network of Chinese scholars in management research. Scientometrics, 98(2), 1435–1454. Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

Authors and Affiliations

  1. 1.Johnson-Shoyama Graduate School of Public PolicyUniversity of Saskatchewan CampusSaskatoonCanada
  2. 2.Departamento de AdministraciónUniversidad Católica del NorteAntofagastaChile

Personalised recommendations