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Biased diffusion on Japanese inter-firm trading network: Estimation of sales from network structure

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  • Hayafumi Watanabe
  • Hideki Takayasu
  • Misako Takayasu
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    Abstract

    To investigate the actual phenomena of transport on a complex network, we analysed empirical data for an inter-firm trading network, which consists of about one million Japanese firms and the sales of these firms (a sale corresponds to the total in-flow into a node). First, we analysed the relationships between sales and sales of nearest neighbourhoods from which we obtain a simple linear relationship between sales and the weighted sum of sales of nearest neighbourhoods (i.e., customers). In addition, we introduce a simple money transport model that is coherent with this empirical observation. In this model, a firm (i.e., customer) distributes money to its out-edges (suppliers) proportionally to the in-degree of destinations. From intensive numerical simulations, we find that the steady flows derived from these models can approximately reproduce the distribution of sales of actual firms. The sales of individual firms deduced from the money-transport model are shown to be proportional, on an average, to the real sales.

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    File URL: http://arxiv.org/pdf/1111.4852
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1111.4852.

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    Date of creation: Nov 2011
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    Publication status: Published in New J. Phys. 14 (2012) 043034
    Handle: RePEc:arx:papers:1111.4852

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    Web page: http://arxiv.org/

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    1. Yoshi Fujiwara & Corrado Di Guilmi & Hideaki Aoyama & Mauro Gallegati & Wataru Souma, 2003. "Do Pareto-Zipf and Gibrat laws hold true? An analysis with European Firms," Papers cond-mat/0310061, arXiv.org, revised Nov 2003.
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