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The Structure and Growth of Weighted Networks

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  • Massimo Riccaboni
  • Stefano Schiavo

Abstract

We develop a simple theoretical framework for the evolution of weighted networks that is consistent with a number of stylized features of real-world data. In our framework, the Barabasi-Albert model of network evolution is extended by assuming that link weights evolve according to a geometric Brownian motion. Our model is verified by means of simulations and real world trade data. We show that the model correctly predicts the intensity and growth distribution of links, the size-variance relationships of the growth of link weights, the relationship between the degree and strength of nodes, as well as the scale-free structure of the network.

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File URL: http://arxiv.org/pdf/0908.0348
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Bibliographic Info

Paper provided by arXiv.org in its series Papers with number 0908.0348.

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Date of creation: Aug 2009
Date of revision: Dec 2009
Handle: RePEc:arx:papers:0908.0348

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References

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  1. Giorgio Fagiolo & Javier Reyes & Stefano Schiavo, 2008. "The World-Trade Web: Topological Properties, Dynamics, and Evolution," LEM Papers Series 2008/16, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
  2. De Fabritiis, Gianni & Riccaboni, Massimo & Pammolli, Fabio, 2003. "On Size and Growth of Business Firms," MPRA Paper 15866, University Library of Munich, Germany.
  3. Elhanan Helpman & Marc Melitz & Yona Rubinstein, 2008. "Estimating Trade Flows: Trading Partners and Trading Volumes," The Quarterly Journal of Economics, MIT Press, vol. 123(2), pages 441-487, 05.
  4. Yamasaki, Kazuko & Matia, Kaushik & Buldyrev, Sergey V. & Fu, Dongfeng & Pammolli, Fabio & Riccaboni, Massimo & Stanley, H. Eugene, 2004. "Preferential attachment and growth dynamics in complex systems," MPRA Paper 15908, University Library of Munich, Germany, revised 06 Feb 2006.
  5. Garlaschelli, Diego & Battiston, Stefano & Castri, Maurizio & Servedio, Vito D.P. & Caldarelli, Guido, 2005. "The scale-free topology of market investments," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 350(2), pages 491-499.
  6. Massimo Riccaboni & Fabio Pammolli & Sergey V. Buldyrev & Linda Ponta & H. Eugene Stanley, 2009. "The Size Variance Relationship of Business Firm Growth Rates," DISA Working Papers 0901, Department of Computer and Management Sciences, University of Trento, Italy, revised 11 Jun 2009.
  7. Thomas Chaney, 2008. "Distorted Gravity: The Intensive and Extensive Margins of International Trade," American Economic Review, American Economic Association, vol. 98(4), pages 1707-21, September.
  8. Giorgio Fagiolo & Mauro Napoletano & Andrea Roventini, 2006. "Are Output Growth-Rate Distributions Fat-Tailed? Some Evidence from OECD Countries," Working Papers 36, University of Verona, Department of Economics.
  9. Giorgio Fagiolo & Javier Reyes & Stefano Schiavo, 2007. "On the Topological Properties of the World Trade Web: A Weighted Network Analysis," Papers 0708.4359, arXiv.org.
  10. Robert C. Feenstra & Robert E. Lipsey & Haiyan Deng & Alyson C. Ma & Hengyong Mo, 2005. "World Trade Flows: 1962-2000," NBER Working Papers 11040, National Bureau of Economic Research, Inc.
  11. Dongfeng Fu & Fabio Pammolli & S. V. Buldyrev & Massimo Riccaboni & Kaushik Matia & Kazuko Yamasaki & H. E. Stanley, 2005. "The Growth of Business Firms: Theoretical Framework and Empirical Evidence," Papers physics/0512005, arXiv.org.
  12. Sergey V. Buldyrev & Jakub Growiec & Fabio Pammolli & Massimo Riccaboni & H. Eugene Stanley, 2007. "The Growth of Business Firms: Facts and Theory," Journal of the European Economic Association, MIT Press, vol. 5(2-3), pages 574-584, 04-05.
  13. D. Garlaschelli & M. I. Loffredo, 2004. "Fitness-dependent topological properties of the World Trade Web," Papers cond-mat/0403051, arXiv.org, revised Oct 2004.
  14. Growiec, Jakub & Pammolli, Fabio & Riccaboni, Massimo & Stanley, H. Eugene, 2008. "On the size distribution of business firms," Economics Letters, Elsevier, vol. 98(2), pages 207-212, February.
  15. K. Bhattacharya & G. Mukherjee & J. Saramaki & K. Kaski & S. S. Manna, 2007. "The International Trade Network: weighted network analysis and modelling," Papers 0707.4343, arXiv.org, revised Mar 2008.
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Citations

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Cited by:
  1. Massimo Riccaboni & Stefano Schiavo, 2009. "The Structure and Growth of International Trade," Documents de Travail de l'OFCE 2009-24, Observatoire Francais des Conjonctures Economiques (OFCE).
  2. Massimo Riccaboni & Stefano Schiavo, 2013. "Stochastic Trade Networks," Working Papers 1/2013, IMT Institute for Advanced Studies Lucca, revised Jan 2013.
  3. Marco Duenas & Giorgio Fagiolo, 2011. "Modeling the International-Trade Network: A Gravity Approach," LEM Papers Series 2011/25, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.

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