Abstract
The aim of this paper is to explore the power-law relationship between the publishing size of complex innovation systems and their citation-based impact. We analyzed articles and reviews from InCites™ database published by six complex innovation systems. We found scale-invariant properties in the complex innovation systems which were analyzed. These properties are evidenced in the power law correlation between complex innovation systems’ citation-based impact and their size with a scaling exponent α ≈ 1.19 ± 0.01. The results suggest citations to a complex innovation system tend to increase 21.19 or 2.28 times when the system doubles its size over time. These scale-invariant emergent properties are a common property of a complex innovation system. These properties can be quantified using the parameters of scale-invariant correlation. These parameters can be used to formulate measures and models useful for informing public policy about scale-invariant emerging properties of a complex innovation system, making comparisons of citation impact between complex systems of vastly different sizes, evaluating citation impact of complex innovation systems according to their size, long range planning, and elaborating rankings across complex innovation systems.
Similar content being viewed by others
Notes
The X min value is the highest probability point in the distribution where the power-law begins.
References
Baranger, M. (2001). Chaos, complexity, and entropy: A physics talk for non-physicists. Wesleyan University Physics Dept. Colloquium, available at http://necsi.org/projects/baranger/cce.pdf.
Bar-Yam, Y. (1997). Dynamics of complex systems. Boston, MA: Addison-Wesley Inc.
Brzezinski, M. (2015). Power laws in citation distributions: Evidence from Scopus. Scientometrics, 103(1), 213–228. doi:10.1007/s11192-014-1524-z.
Clauset, A., Shalizi, C. R., & Newman, M. E. J. (2009). Power-law distributions in empirical data. SIAM Review, 51(4), 661–703. doi:10.1137/070710111.
Coccia, M., & Bozeman, B. (2016). Allometric models to measure and analyze the evolution of international research collaboration. Scientometrics, 108(3), 1065–1084. doi:10.1007/s11192-016-2027-x.
Coccia, M., & Wang, L. (2016). Evolution and convergence of the patterns of international scientific collaboration. Proceedings of the National Academy of Sciences of the United States of America, 113(8), 2057–2061. doi:10.1073/pnas.1510820113.
Egghe, L. (2005). The power of power laws and an interpretation of lotkaian informetric systems as self-similar fractals. Journal of the American Society for Information Science and Technology, 56(7), 669–675. doi:10.1002/asi.20158.
Egghe, L., & Rousseau, R. (1986). A characterization of distributions which satisfy Price’s Law and consequences for the Laws of Zipf and Mandelbrot. Journal of Information Science, 12(4), 193–197. doi:10.1177/016555158601200406.
Egghe, L., Liang, L. M., & Rousseau, R. (2009). A relation between h-index and impact factor in the power-law model. Journal of the American Society for Information Science and Technology, 60(11), 2362–2365. doi:10.1002/asi.21144.
Frame, J. D., & Carpenter, M. P. (1979). International research collaboration. Social Studies of Science, 2, 481–497.
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. doi:10.1073/pnas.122653799.
Katz, J. S. (1999). The self-similar science system. Research Policy, 28(5), 501–517. doi:10.1016/S0048-7333(99)00010-4.
Katz, J. S. (2000). Scale-independent indicators and research evaluation. Science and Public Policy, 27(1), 23–36. doi:10.3152/147154300781782156.
Katz, J. S. (2005). Scale-independent bibliometric indicators. Measurement, 3(1), 24–28. doi:10.1207/s15366359mea0301_3.
Katz, J. S. (2006). Indicators for complex innovation systems. Research Policy, 35(7), 893–909. doi:10.1016/j.respol.2006.03.007.
Katz, J. S. (2012a). Scale-independent measures: Theory and practice. In Paper presented at the 17th International Conference on Science and Technology Indicators, September 5–8, Montreal, Canada. http://sticonference.org/index.php?page=proc.
Katz, J. S. (2012b). Scale-independent measures: Theory and practice. Retrieved from http://www.sussex.ac.uk/spru/jskatz.
Katz, J. S. (2016a). Policies considerations for evidence-based measures of complex innovation systems. In Paper presented at the SPRU 50th Aniversary Conference, University of Sussex, Brighton, UK.
Katz, J. S. (2016b). What is a complex innovation system? PLoS ONE, 11(6), e0156150. doi:10.1371/journal.pone.0156150.
Kwapień, J., & Drożdż, S. (2012). Physical approach to complex systems. Physics Reports, 515(3–4), 115–226. doi:10.1016/j.physrep.2012.01.007.
Leguendre, P., & Leguendre, L. (2012). Numerical ecology (3rd ed., Vol. 24). Great Britain: Elsevier B. V.
Lotka, A. J. (1926). The frecuency distribution of scientific productivity. Journal of the Academy of Sciences, 16(1), 317–323.
Marković, D., & Gros, C. (2014). Power laws and self-organized criticality in theory and nature. Physics Reports, 536(2), 41–74. doi:10.1016/j.physrep.2013.11.002.
Mayernik, M. (2010). The distributions of MARC fields in bibliographic records a power law analysis. Library Resources & Technical Services, 54(1), 40–54. doi:10.5860/lrts.54n1.40.
Milojevic, S. (2010). Power law distributions in information science: Making the case for logarithmic binning. Journal of the American Society for Information Science and Technology, 61(12), 2417–2425. doi:10.1002/asi.21426.
Naranan, S. (1971). Power law relations in science bibliography—a self-consistent interpretation. Journal of Documentation, 27(2), 83–97. doi:10.1108/eb026510.
Newman, M. E. J. (2001). Scientific collaboration networks. I. Network construction and fundamental results. Physical Review E, Statistical, Nonlinear, and Soft Matter Physics, 64(1 Pt 2), 016131. doi:10.1103/PhysRevE.64.016131.
Newman, M. E. J. (2004). Coauthorship networks and patterns of scientific collaboration. Proceedings of the National Academy of Sciences USA, 101 Suppl 1(supplement 1), 5200–5205. doi:10.1073/pnas.0307545100.
Newman, M. E. J. (2005). Power laws, Pareto distributions and Zipf’s law. Contemporary Physics, 46(5), 323–351. doi:10.1080/00107510500052444.
Newman, M. E. J. (2011). [SIGMETRICS posting. http://mail.asis.org/mailman/private/sigmetrics/2011-September/005797.html].
Reuters, T. (2016). InCites indicators handbook. In T. Reuters (Ed.), (pp. 27). https://incites.thomsonreuters.com/: Thomson Reuters.
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. doi:10.1002/asi.23575.
Ronda-Pupo, G. A., & Katz, J. S. (2016b). The scaling relationship between citation-based performance and scientific collaboration in natural sciences. Journal of the Association for Information Science and Technology, in Early view.. doi:10.1002/asi.23759.
Sahal, D. (1981). Patterns of technological innovation. New York, NY: Addison-Wesley.
Smith, R. J. (2009). Use and misuse of the reduced major axis for line-fitting. American Journal of Physical Anthropology, 140(3), 476–486. doi:10.1002/ajpa.21090.
Sutter, M., & Kocher, M. G. (2001). Power laws of research output. Evidence for journals of economics. Scientometrics, 51(2), 405–414. doi:10.1023/a:1012757802706.
Thelwall, M. (2016a). Are the discretised lognormal and hooked power law distributions plausible for citation data? Journal of Informetrics, 10(2), 454–470. doi:10.1016/j.joi.2016.03.001.
Thelwall, M. (2016b). Are there too many uncited articles? Zero inflated variants of the discretised lognormal and hooked power law distributions. Journal of Informetrics, 10(2), 622–633. doi:10.1016/j.joi.2016.04.014.
Thelwall, M. (2016c). The discretised lognormal and hooked power law distributions for complete citation data: Best options for modelling and regression. Journal of Informetrics, 10(2), 336–346. doi:10.1016/j.joi.2015.12.007.
van Raan, A. F. J. (2008a). Bibliometric statistical properties of the 100 largest European research universities: Prevalent scaling rules in the science system. Journal of the American Society for Information Science and Technology, 59(3), 461–475. doi:10.1002/asi.20761.
van Raan, A. F. J. (2008b). Scaling rules in the science system: Influence of field-specific citation characteristics on the impact of research groups. Journal of the American Society for Information Science and Technology, 59(4), 565–576. doi:10.1002/asi.20765.
van Raan, A. F. J. (2013). Universities scale like cities. PLoS ONE, 8(3), e59384. doi:10.1371/journal.pone.0059384.
Vicsek, T. (2002). The bigger picture. Nature, 418(6894), 131. doi:10.1038/418131a.
Warton, D. I., Wright, I. J., Falster, D. S., & Westoby, M. (2006). Bivariate line-fitting methods for allometry. Biological Reviews of the Cambridge Philosophical Society, 81(2), 259–291. doi:10.1017/S1464793106007007.
Ye, F. Y., & Rousseau, R. (2008). The power law model and total career h-index sequences. Journal of Informetrics, 2(4), 288–297. doi:10.1016/j.joi.2008.09.002.
Zhao, S. X., & Ye, F. Y. (2013). Power-law link strength distribution in paper cocitation networks. Journal of the American Society for Information Science and Technology, 64(7), 1480–1489. doi:10.1002/asi.22846.
Acknowledgements
We thank Professor J. Sylvan Katz for all his teachings on power law analysis, Professor Mario Coccia for insightful comments and two anonymous reviewers for interesting suggestions on a previous version of the manuscript. Funding was provided by Ministerio de Economía y Competitividad de España (Grant No. ECO-2015-67434-r).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ronda-Pupo, G.A. The citation-based impact of complex innovation systems scales with the size of the system. Scientometrics 112, 141–151 (2017). https://doi.org/10.1007/s11192-017-2401-3
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11192-017-2401-3