The international-trade network: gravity equations and topological properties

  • 881 Accesses

  • 71 Citations


This paper begins to explore the determinants of the topological properties of the international-trade network (ITN). We fit bilateral-trade flows using a standard gravity equation to build a “residual” ITN where trade-link weights are depurated from geographical distance, size, border effects, trade agreements, and so on. We then compare the topological properties of the original and residual ITNs. We find that the residual ITN displays, unlike the original one, marked signatures of a complex system, and is characterized by a very different topological architecture. Whereas the original ITN is geographically clustered and organized around a few large-sized hubs, the residual ITN displays many small-sized but trade-oriented countries that, independently of their geographical position, either play the role of local hubs or attract large and rich countries in relatively complex trade-interaction patterns.

This is a preview of subscription content, log in to check access.

Access options

Buy single article

Instant unlimited access to the full article PDF.

US$ 39.95

Price includes VAT for USA

Subscribe to journal

Immediate online access to all issues from 2019. Subscription will auto renew annually.

US$ 99

This is the net price. Taxes to be calculated in checkout.


  1. Abeysinghe T, Forbes K (2005) Trade linkages and output-multiplier effects: a structural var approach with a focus on asia. Rev Int Econ 13: 356–375

  2. Albert R, Barabási A-L (2002) Statistical mechanics of complex networks. Rev Mod Phys 74: 47–97

  3. Anderson JE (1979) A theoretical foundation for the gravity equation. Am Econ Rev 69: 106–116

  4. Anderson JE, van Wincoop E (2003) Gravity with gravitas: a solution to the border puzzle. Am Econ Rev 93: 170–192

  5. Artis M, Galvão A-B, Marcellino M (2003) The transmission mechanism in a changing world. Economics working papers ECO2003/18. European University Institute

  6. Baier SL, Bergstrand JH (2007) Do free trade agreements actually increase members’ international trade?. J Int Econ 71: 72–95

  7. Baldwin R, Taglioni D (2006) Gravity for dummies and dummies for gravity equations. NBER working papers 12516. National Bureau of Economic Research

  8. Barrat A, Barthélemy M, Pastor-Satorras R, Vespignani A (2004) The architecture of complex weighted networks. Proc Natl Acad Sci 101: 3747–3752

  9. Barthélemy M, Barrat A, Pastor-Satorras R, Vespignani A (2005) Characterization and modeling of complex weighted networks. Physica A 346: 34–43

  10. Bergstrand JH (1985) The gravity equation in international trade: some microeconomic foundations and empirical evidence. Rev Econ Stat 67: 474–481

  11. Bhattacharya K, Mukherjee G, Manna S (2007) The international trade network. In: Chatterjee A, Chakrabarti B (eds) Econophysics of markets and business networks. Springer, Milan

  12. Bhattacharya K, Mukherjee G, Sarämaki J, Kaski K, Manna S (2008) The international trade network: weighted network analysis and modeling. J Stat Mech Theory Exp A 2: P02002

  13. Bhavnani R, Coe DT, Subramanian A, Tamirisa NT (2002) The missing globalization puzzle. IMF working papers 02/171. International Monetary Fund

  14. Burger M, Oort Fv, Linders G (2009) On the specification of the gravity model of trade: zeros, excess zeros and zero-inflated estimation. Research Paper ERS-2009-003-ORG Revision. Erasmus Research Institute of Management (ERIM)

  15. Cormen TH, Leiserson CE, Rivest RL, Stein C (2001) Introduction to algorithms. MIT Press and McGraw-Hill, Cambridge and New York

  16. Deardorff A (1998) Determinants of bilateral trade: does gravity work in a neoclassical world? In: The regionalization of the world economy. NBER Chapters. National Bureau of Economic Research, pp 7–32

  17. DeMontis A, Barthélemy M, Chessa A, Vespignani A (2005) The structure and evolution of inter-urban traffic: a weighted network analysis. Environ Plan B Plan Design 34: 905–924

  18. Dorogovtsev S, Mendes J (2003) Evolution of networks: from biological nets to the internet and WWW. Oxford University Press, Oxford

  19. Eichengreen B, Irwin DA (1996) The role of history in bilateral trade flows. NBER Working Papers 5565. National Bureau of Economic Research

  20. Fagiolo G (2007) Clustering in complex directed networks. Phys Rev E 76: 026107

  21. Fagiolo G, Schiavo S, Reyes J (2008) On the topological properties of the world trade web: a weighted network analysis. Physica A 387: 3868–3873

  22. Fagiolo G, Schiavo S, Reyes J (2009a) The ecolution of the world trade web: a weighted-network approach. J Evol Econ (forthcoming)

  23. Fagiolo G, Schiavo S, Reyes J (2009b) World-trade web: Topological properties, dynamics, and evolution. Physical Review E 79: 036115

  24. Feenstra RC, Markusen JR, Rose AK (2001) Using the gravity equation to differentiate among alternative theories of trade. Can J Econ 34: 430–447

  25. Fisher E, Vega-Redondo F (2006) The linchpins of a modern economy. Working paper. Cal Poly

  26. Forbes K (2002) Are trade linkages important determinants of country vulnerability to crises?. In: Sebastian E, Jeffrey F (eds) Preventing currency crises in emerging markets. University of Chicago Press, Chicago

  27. Frankel J (1997) Regional trading blocs in the world economic system. Institute for International Economics, Washington DC

  28. Fratianni M (2009) The gravity model in international trade. In: Rugman AM (eds) The Oxford handbook of international business. Oxford University Press, Oxford

  29. Garlaschelli D, Di Matteo T, Aste T, Caldarelli G, Loffredo M (2007) Interplay between topology and dynamics in the world trade web. Eur Phys J B 57: 1434–6028

  30. Garlaschelli D, Loffredo M (2004) Fitness-dependent topological properties of the world trade web. Phys Rev Lett 93: 188701

  31. Garlaschelli D, Loffredo M (2005) Structure and evolution of the world trade network. Physica A 355: 138–144

  32. Gleditsch K (2002) Expanded trade and GDP data. J Conflict Resolut 46: 712–724

  33. Glick R, Rose AK (2001) Does a currency union affect trade? The time series evidence. NBER working papers 8396. National Bureau of Economic Research

  34. Gower JC, Ross GJS (1969) Minimum spanning trees and single linkage cluster analysis. Appl Stat 18: 54–64

  35. Hayfield T, Racine JS (2008) Nonparametric econometrics: the np package. J Stat Softw 27

  36. Helliwell JF, Padmore T (1985) Empirical studies of macroeconomic interdependence. In: Jones R, Kenen P (eds) Hand book of international economies. Elsevier, Amsterdam, The Netherlands

  37. Hurvich C, Simonoff J, Tsai C (1998) Smoothing parameter selection in nonparametric regression using an improved akaike information criterion. J Royal Stat Soc Series B 60: 271–293

  38. Jackson MO, Demange G, Goyal S, Nouwel AVD (2003) A survey of models of network formation: stability and efficiency. In: In group formation in economics: networks, clubs and coalitions. Cambridge University Press, Cambridge

  39. Kali R, Méndez F, Reyes J (2007) Trade structure and economic growth. J Int Trade Econ Dev 16: 245–269

  40. Kali R, Reyes J (2007) The architecture of globalization: a network approach to international economic integration. J Int Bus Stud 38: 595–620

  41. Krempel L, Pluemper T (2003) Exploring the dynamics of international trade by combining the comparative advantages of multivariate statistics and network visualizations. J Soc Struct 4: 1–22

  42. Krugman P (1995) Growing world trade: causes and consequences. Brookings Pap Econ Act 26: 327–377

  43. Leamer EE, Levinsohn J (1995) International trade theory: the evidence (chapter 26). In: Grossman GM, Rogoff K (eds) Handbook of international economics, vol 3 of handbook of international economics. Elsevier. pp 1339–1394

  44. Li Q, Racine J (2004) Cross-validated local linear nonparametric regression. Statistica Sinica 14: 485–512

  45. Li X, Jin YY, Chen G (2003) Complexity and synchronization of the world trade web. Physica A Stat Mech Appl 328: 287–296

  46. Linders G-JM, de Groot HL (2006) Estimation of the gravity equation in the presence of zero flows. Tinbergen Institute discussion papers 06-072/3. Tinbergen Institute

  47. Mantegna R (1999) Hierarchical structure in financial markets. Eur Phys J B 11: 193–197

  48. Mitzenmacher M (2004) A brief history of generative models for power law and lognormal distributions. Internet Math 1: 226–251

  49. Newman M (2005) A measure of betweenness centrality based on random walks. Soc Networks 27: 39–54

  50. Overman HG, Redding S, Venables AJ (2003) The economic geography of trade, production, and income: a survey of empirics. In: Harrigan J, Choi K (eds) Handbook of international trade. Blackwell Publishers, Oxford, pp 353–387

  51. Reichardt J, White D (2007) Role models for complex networks. Eur Phys J B 60: 217–224

  52. Reyes J, Schiavo S, Fagiolo G (2008) Assessing the evolution of international economic integration using random-walk betweenness centrality: the cases of East Asia and Latin America. Adv Complex Syst 11: 685–702

  53. Rose AK (2000) One money, one market: the effects of common currency on trade. Econ Policy 30: 9–45

  54. Rose AK, Spiegel MM (2002) A gravity model of sovereign lending: trade, default and credit. Working papers in applied economic theory 2002–09. Federal Reserve Bank of San Francisco

  55. Rosser JB (2008) Econophysics and economic complexity. Adv Complex Syst 11: 745–760

  56. Santos Silva JMC, Tenreyro S (2006) The log of gravity. Rev Econ Stat 88: 641–658

  57. Saramaki J, Kivelä M, Onnela J, Kaski K, Kertész J (2007) Generalizations of the clustering coefficient to weighted complex networks. Phys Rev E 75: 027105

  58. Serrano A, Boguñá M (2003) Topology of the world trade web. Phys Rev E 68: 015101(R)

  59. Serrano A, Boguñá M, Vespignani A (2007) Patterns of dominant flows in the world trade web. J Econ Interact Coord 2: 111–124

  60. Stanley MHR, Buldyrev SV, Havlin S, Mantegna RN, Salinger MA, Eugene Stanley H (1995) Zipf plots and the size distribution of firms. Econ Lett 49: 453–457

  61. StataCorp: (2007) Stata statistical software: release 10. StataCorp LP, College Station

  62. Sutton J (1997) Gibrat’s legacy. J Econ Lit 35: 40–59

  63. Tzekina I, Danthi K, Rockmore D (2008) Evolution of community structure in the world trade web. Eur Phys J B Condens Matter 63: 541–545

  64. Vuong QH (1989) Likelihood ratio tests for model selection and non-nested hypotheses. Econometrica 57: 307–333

  65. Watts D, Strogatz S (1998) Collective dynamics of ‘small-world’ networks. Nature 393: 440–442

  66. Wooldridge JM (2001) Econometric analysis of cross section and panel data. The MIT Press, Boston

Download references

Author information

Correspondence to Giorgio Fagiolo.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Fagiolo, G. The international-trade network: gravity equations and topological properties. J Econ Interact Coord 5, 1–25 (2010) doi:10.1007/s11403-010-0061-y

Download citation


  • International trade network
  • Gravity equation
  • Weighted network analysis
  • Topological properties
  • Econophysics

JEL Classification

  • F10
  • D85