Null models of economic networks: the case of the world trade web

  • Giorgio Fagiolo
  • Tiziano Squartini
  • Diego Garlaschelli
Regular Article


In all empirical-network studies, the observed properties of economic networks are informative only if compared with a well-defined null model that can quantitatively predict the behavior of such properties in constrained graphs. However, predictions of the available null-model methods can be derived analytically only under assumptions (e.g., sparseness of the network) that are unrealistic for most economic networks like the world trade web (WTW). In this paper we study the evolution of the WTW using a recently-proposed family of null network models. The method allows to analytically obtain the expected value of any network statistic across the ensemble of networks that preserve on average some local properties, and are otherwise fully random. We compare expected and observed properties of the WTW in the period 1950–2000, when either the expected number of trade partners or total country trade is kept fixed and equal to observed quantities. We show that, in the binary WTW, node-degree sequences are sufficient to explain higher-order network properties such as disassortativity and clustering-degree correlation, especially in the last part of the sample. Conversely, in the weighted WTW, the observed sequence of total country imports and exports are not sufficient to predict higher-order patterns of the WTW. We discuss some important implications of these findings for international-trade models.


World trade web Null models of networks Complex networks International trade 

JEL Classification

D85 C49 C63 F10 



G.F. gratefully acknowledges financial support received by the research project “The international trade network: empirical analyses and theoretical models” ( funded by the Italian Ministry of Education, University and Research (Scientific Research Programs of National Relevance 2009). D.G. gratefully acknowledges support by the Dutch Econophysics Foundation (Stichting Econpophysics Leiden, The Netherlands), with funds from beneficiaries of Duyfken Trading Knowledge BV, Amsterdam, The Netherlands. T.S. acknowledges support from an ERC Advanced Investigator Grant.


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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • Giorgio Fagiolo
    • 1
  • Tiziano Squartini
    • 2
    • 3
  • Diego Garlaschelli
    • 3
  1. 1.Laboratory of Economics and ManagementSant’Anna School of Advanced StudiesPisaItaly
  2. 2.CSC and Department of PhysicsUniversity of SienaSienaItaly
  3. 3.Instituut-Lorentz for Theoretical Physics, Leiden Institute of PhysicsUniversity of LeidenLeidenThe Netherlands

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