Google matrix analysis of the multiproduct world trade network

  • Leonardo Ermann
  • Dima L. Shepelyansky
Regular Article


Using the United Nations COMTRADE database [United Nations Commodity Trade Statistics Database, available at: Accessed November (2014)] we construct the Google matrix G of multiproduct world trade between the UN countries and analyze the properties of trade flows on this network for years 1962−2010. This construction, based on Markov chains, treats all countries on equal democratic grounds independently of their richness and at the same time it considers the contributions of trade products proportionally to their trade volume. We consider the trade with 61 products for up to 227 countries. The obtained results show that the trade contribution of products is asymmetric: some of them are export oriented while others are import oriented even if the ranking by their trade volume is symmetric in respect to export and import after averaging over all world countries. The construction of the Google matrix allows to investigate the sensitivity of trade balance in respect to price variations of products, e.g. petroleum and gas, taking into account the world connectivity of trade links. The trade balance based on PageRank and CheiRank probabilities highlights the leading role of China and other BRICS countries in the world trade in recent years. We also show that the eigenstates of G with large eigenvalues select specific trade communities.


Statistical and Nonlinear Physics 


  1. 1.
    United Nations Commodity Trade Statistics Database, Accessed November 2014
  2. 2.
    World Trade Organization, International Trade Statistics 2014, Accessed November 2014
  3. 3.
    P.R. Krugman, M. Obstfeld, M. Melitz, International Economics: Theory & Policy (Prentice Hall, New Jersey, 2011)Google Scholar
  4. 4.
    S. Dorogovtsev, Lectures on Complex Networks (Oxford University Press, Oxford, 2010)Google Scholar
  5. 5.
    S. Brin, L. Page, Computer Networks and ISDN Systems 30, 107 (1998)CrossRefGoogle Scholar
  6. 6.
    A.M. Langville, C.D. Meyer, Google’s PageRank and Beyond: the Science of Search Engine Rankings (Princeton University Press, Princeton, 2006)Google Scholar
  7. 7.
    A.D. Chepelianskii, arXiv:1003.5455[cs.SE] (2010)Google Scholar
  8. 8.
    A.O. Zhirov, O.V. Zhirov, D.L. Shepelyansky, Eur. Phys. J. B 77, 523 (2010)CrossRefADSGoogle Scholar
  9. 9.
    L. Ermann, K.M. Frahm, D.L. Shepelyansky, arXiv:1409.0428[physics.soc-ph] (2014)Google Scholar
  10. 10.
    Web page Maps of the world, Accessed December 2014
  11. 11.
    L. Ermann, D.L. Shepelyansky, Acta Phys. Pol. A 120, A158 (2011)Google Scholar
  12. 12.
    L. Ermann, D.L. Shepelyansky, Phys. Lett. A 377, 250 (2013)CrossRefADSMATHGoogle Scholar
  13. 13.
    D. Garlaschelli, M.I. Loffredo, Physica A 355, 138 (2005)CrossRefADSMathSciNetGoogle Scholar
  14. 14.
    M.A. Serrano, M. Boguna, A. Vespignani, J. Econ. Interac. Coord. 2, 111 (2007)CrossRefGoogle Scholar
  15. 15.
    G. Fagiolo, J. Reyes, S. Schiavo, Phys. Rev. E 79, 036115 (2009)CrossRefADSMathSciNetGoogle Scholar
  16. 16.
    J. He, M.W. Deem, Phys. Rev. Lett. 105, 198701 (2010)CrossRefADSGoogle Scholar
  17. 17.
    G. Fagiolo, J. Reyes, S. Schiavo, J. Evol. Econ. 20, 479 (2010)CrossRefGoogle Scholar
  18. 18.
    M. Barigozzi, G. Fagiolo, D. Garlaschelli, Phys. Rev. E 81, 046104 (2010)CrossRefADSGoogle Scholar
  19. 19.
    T. Squartini, G. Fagiolo, D. Garlaschelli, Phys. Rev. E 84, 046118 (2011)CrossRefADSGoogle Scholar
  20. 20.
    L. De Benedictis, L. Tajoli, World Econ. 34, 1417 (2011)Google Scholar
  21. 21.
    T. Deguchi, K. Takahashi, H. Takayasu, M. Takayasu, PLoS One 9, e1001338 (2014)CrossRefGoogle Scholar
  22. 22.
    C.A. Hidalgo, B. Klinger, A.-L. Barabási, R. Hausmann, Science 317, 5837 (2007)CrossRefGoogle Scholar
  23. 23.
    J.-P. Bouchaud, M. Potters, Theory of Financial Risk and Derivative Pricing (Cambridge University Press, Cambridge, 2003)Google Scholar
  24. 24.
    M.C. Munnix, R. Schaefer, T. Guhr, PLoS One 9, e98030 (2014)CrossRefADSGoogle Scholar
  25. 25.
    Web page Google matrix of multiproduct world trade, Accessed December 2014
  26. 26.
    L. Ermann, K.M. Frahm, D.L. Shepelyansky, Eur. Phys. J. B 86, 193 (2013)CrossRefADSMathSciNetGoogle Scholar
  27. 27.
    K. Soramäki, M.L. Bech, J. Arnold, R.J. Glass, W.E. Beyler, Physica A 379, 317 (2007)CrossRefADSGoogle Scholar
  28. 28.
    B. Craig, G. von Peter, Interbank tiering and money center bank, Discussion paper No. 12, Deutsche Bundesbank (2010)Google Scholar
  29. 29.
    R.J. Garratt, L. Mahadeva, K. Svirydzenka, Mapping systemic risk in the international banking network, Working paper No. 413, Bank of England (2011)Google Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Departamento de Física TeóricaGIyA, CNEABuenos AiresArgentina
  2. 2.Laboratoire de Physique Théorique du CNRS, IRSAMCUniversité de Toulouse, UPSToulouseFrance

Personalised recommendations