Google Matrix of the World Trade Network

• Authors: L. Ermann , D. Shepelyansky
• Languages of publication: EN

Abstracts

EN

Using the United Nations Commodity Trade Statistics Database we construct the Google matrix of the world trade network and analyze its properties for various trade commodities for all countries and all available years from 1962 to 2009. The trade flows on this network are classified with the help of PageRank and CheiRank algorithms developed for the World Wide Web and other large scale directed networks. For the world trade this ranking treats all countries on equal democratic grounds independent of country richness. Still this method puts at the top a group of industrially developed countries for trade in all commodities. Our study establishes the existence of two solid state like domains of rich and poor countries which remain stable in time, while the majority of countries are shown to be in a gas like phase with strong rank fluctuations. A simple random matrix model provides a good description of statistical distribution of countries in two-dimensional rank plane. The comparison with usual ranking by export and import highlights new features and possibilities of our approach.

Keywords

EN

89.65.Gh; 89.75.Hc; 89.75.-k; 89.20.Hh

Discipline

• 89.75.-k: Complex systems(for complex chemical systems, see 82.40.Qt; for biological complexity, see 87.18.-h)
• 89.75.Hc: Networks and genealogical trees
• 89.20.Hh: World Wide Web, Internet
• 89.65.Gh: Economics; econophysics, financial markets, business and management(for economic issues regarding production and use of renewable energy, see 88.05.Lg)

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2011
• Volume: 120
• Issue: 6A
• Pages: A-158-A-171

Dates

published

2011-12

Contributors

author

L. Ermann

• Laboratoire de Physique Théorique du CNRS, IRSAMC, Université de Toulouse, UPS, 31062 Toulouse, France

author

D. Shepelyansky

• Laboratoire de Physique Théorique du CNRS, IRSAMC, Université de Toulouse, UPS, 31062 Toulouse, France

References

• [1] P.R. Krugman, M. Obstfeld, M. Melitz, International Economics: Theory & Policy, Prentice Hall, New Jersey 2011
• [2] Central Intelligence Agency, The CIA World Factbook 2010, Skyhorse Publ. Inc., New York 2009
• [3] S. Brin, L. Page, Computer Networks ISDN Syst. 30, 107 (1998)
• [4] A.M. Langville, C.D. Meyer, Google's PageRank and Beyond: The Science of Search Engine Rankings, Princeton University Press, Princeton 2006
• [5] N. Litvak, W.R.W. Scheinhardt, Y. Volkovich, Lecture Notes Comput. Sci. 4936, 72 (2008)
• [6] D. Donato, L. Laura, S. Leonardi, S. Millozzi, Eur. Phys. J. B 38, 239 (2004)
• [7] G. Pandurangan, P. Raghavan, E. Upfal, Internet Math. 3, 1 (2005)
• [8] S. Redner, Physics Today 58, 49 (2005)
• [9] F. Radicchi, S. Fortunato, B. Markines, A. Vespignani, Phys. Rev. E 80, 056103 (2009)
• [10] J. West, T. Bergstrom, C.T. Bergstrom, arXiv:0911.1807, to appear in J. Am. Soc. Info. Sci. Tech. (2011); http://eigenfactor.org/
• [11] A.D. Chepelianskii, Towards Physical Laws for Software Architecture, arXiv:1003.5455[cs.SE] (2010); http://www.quantware.ups-tlse.fr/QWLIB/linuxnetwork/
• [12] A.O. Zhirov. O.V. Zhirov, D.L. Shepelyansky, Eur. Phys. J. B 77, 523 (2010); http://www.quantware.ups-tlse.fr/QWLIB/2drankwikipedia/
• [13] United Nations Commodity Trade Statistics Database http://comtrade.un.org/db/
• [14] P.B. Slater, Sov. Geography Rev. Trans. 16, 453 (1975)
• [15] P.B. Slater, IEEE Trans. Sys. Man Cyber. 5, 278 (1975)
• [16] D. Garlaschelli, M.I. Loffredo, Physica A, Stat. Mech. Appl. 355, 138 (2005)
• [17] M.A. Serrano, M. Boguna, A. Vespignani, J. Econ. Interac. Coor. 2, 111 (2007)
• [18] L. De Benedictis, L. Tajoli, The World Trade Network, working paper (2009); available at http://www.eief.it/files/2010/10/luca-de-benedictis.pdf
• [19] G. Fagiolo, J. Reyes, S. Schiavo, Phys. Rev. E 79, 036115 (2009)
• [20] J. He, M.W. Deem, Phys. Rev. Lett. 105, 198701 (2010)
• [21] G. Fagiolo, J. Reyes, S. Schiavo, J. Evol. Econ. 20, 479 (2010)
• [22] M. Barigozzi, G. Fagiolo, D. Garlaschelli, Phys. Rev. E 81, 046104 (2010)
• [23] T. Squartini, G. Fagiolo, D. Garlaschelli, Rewiring World Trade. Part II. A Weighted Network Analysis, arXiv:1103.1249[physics.soc-ph] (2011)
• [24] http://www.quantware.ups-tlse.fr/QWLIB/tradecheirank/
• [25] G.K. Zipf, Human Behavior and the Principle of Least Effort, Addison-Wesley, Boston 1949
• [26] K. Avrachenkov, N. Litvak, K. Pham, Internet Math. 5, 47 (2005)
• [27] B. Georgeot, O. Giraud, D.L. Shepelyansky, Phys. Rev. E 81, 056109 (2010)
• [28] D.L. Shepelyansky, O.V. Zhirov, Phys. Rev. E 81, 036213 (2010)
• [29] L. Ermann, D.L. Shepelyansky, Phys. Rev. E 81, 036221 (2010)
• [30] L. Ermann, D.L. Shepelyansky, Eur. Phys. J. B 75, 299 (2010)
• [31] L. Ermann, A.D. Chepelianskii, D.L. Shepelyansky, Eur. Phys. J. B 79, 115 (2011)
• [32] Wikipedia contributors, G-20 Major Economies, Wikipedia, The Free Encyclopedia, Web. 25 Mar. 2011
• [33] S.M. Ulam, A Collection of Mathematical Problems, Vol. 8 of Interscience tracs in pure and applied mathematics, Interscience, New York 1960, p. 73

Identifiers

DOI

10.12693/APhysPolA.120.A-158