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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.

Suggested Citation

  • Massimo Riccaboni & Stefano Schiavo, 2009. "The Structure and Growth of Weighted Networks," Papers 0908.0348, arXiv.org, revised Dec 2009.
  • Handle: RePEc:arx:papers:0908.0348
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    References listed on IDEAS

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    1. 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.
    2. Thomas Chaney, 2008. "Distorted Gravity: The Intensive and Extensive Margins of International Trade," American Economic Review, American Economic Association, vol. 98(4), pages 1707-1721, September.
    3. Giorgio Fagiolo & Mauro Napoletano & Andrea Roventini, 2008. "Are output growth-rate distributions fat-tailed? some evidence from OECD countries," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(5), pages 639-669.
    4. 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.
    5. Fagiolo, Giorgio & Reyes, Javier & Schiavo, Stefano, 2008. "On the topological properties of the world trade web: A weighted network analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(15), pages 3868-3873.
    6. 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.
    7. 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.
    8. De Fabritiis, G. & Pammolli, F. & Riccaboni, M., 2003. "On size and growth of business firms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 38-44.
    9. 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.
    10. 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.
    11. 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.
    12. D. Garlaschelli & M. I. Loffredo, 2004. "Fitness-dependent topological properties of the World Trade Web," Papers cond-mat/0403051, arXiv.org, revised Oct 2004.
    13. 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.
    14. Elhanan Helpman & Marc Melitz & Yona Rubinstein, 2008. "Estimating Trade Flows: Trading Partners and Trading Volumes," The Quarterly Journal of Economics, Oxford University Press, vol. 123(2), pages 441-487.
    15. 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.
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    Citations

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    Cited by:

    1. Massimo Riccaboni & Stefano Schiavo, 2012. "Stochastic Trade Networks," DEGIT Conference Papers c017_014, DEGIT, Dynamics, Economic Growth, and International Trade.
    2. Shamnaaz Sufrauj & Stefano Schiavo & Massimo Riccaboni, 2015. "Big hits, export concentration and volatility," Economia Politica: Journal of Analytical and Institutional Economics, Springer;Fondazione Edison, vol. 32(2), pages 135-166, August.
    3. Takayuki Mizuno & Wataru Souma & Tsutomu Watanabe, 2014. "Buyer-Supplier Networks and Aggregate Volatility," CARF F-Series CARF-F-353, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    4. Massimo Riccaboni & Alessandro Rossi & Stefano Schiavo, 2013. "Global networks of trade and bits," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 8(1), pages 33-56, April.
    5. Zhen Zhu & Greg Morrison & Michelangelo Puliga & Alessandro Chessa & Massimo Riccaboni, 2015. "The Similarity of Global Value Chains: A Network-Based Measure," Papers 1508.04392, arXiv.org.
    6. Atushi Ishikawa & Shouji Fujimoto & Takayuki Mizuno & Tsutomu Watanabe, 2014. "Analytical Derivation of Power Laws in Firm Size Variables from Gibrat’s Law and Quasi-inversion Symmetry: A Geomorphological Approach," UTokyo Price Project Working Paper Series 019, University of Tokyo, Graduate School of Economics.
    7. MIZUNO Takayuki & SOUMA Wataru & WATANABE Tsutomu, 2015. "Buyer-Supplier Networks and Aggregate Volatility," Discussion papers 15056, Research Institute of Economy, Trade and Industry (RIETI).
    8. Marco Dueñas & Giorgio Fagiolo, 2013. "Modeling the International-Trade Network: a gravity approach," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 8(1), pages 155-178, April.
    9. 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).
    10. Sufrauj, Shamnaaz & Schiavo, Stefano & Riccaboni, Massimo, 2014. "The Structure and Growth of World Trade, and the Role of Europe in the Global Economy," MPRA Paper 54122, University Library of Munich, Germany.
    11. Takayuki Mizuno & Wataru Souma & Tsutomu Watanabe, 2014. "The Structure and Evolution of Buyer-Supplier Networks," CARF F-Series CARF-F-339, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    12. Takayuki Mizuno & Wataru Souma & Tsutomu Watanabe, 2014. "Buyer-Supplier Networks and Aggregate Volatility," UTokyo Price Project Working Paper Series 033, University of Tokyo, Graduate School of Economics.
    13. De Benedictis Luca & Nenci Silvia & Santoni Gianluca & Tajoli Lucia & Vicarelli Claudio, 2014. "Network Analysis of World Trade using the BACI-CEPII Dataset," Global Economy Journal, De Gruyter, vol. 14(3-4), pages 1-57, October.
    14. Zhen Zhu & Federica Cerina & Alessandro Chessa & Guido Caldarelli & Massimo Riccaboni, 2014. "The rise of China in the international trade network: a community core detection approach," Working Papers 4/2014, IMT Institute for Advanced Studies Lucca, revised Apr 2014.
    15. Mizuno, Takayuki & Souma, Wataru & Watanabe, Tsutomu, 2014. "The Structure and Evolution of Buyer-Supplier Networks," Working Paper Series 27, Center for Interfirm Network, Institute of Economic Research, Hitotsubashi University.

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