Biased Diffusion on Japanese Inter-firm Trading Network
New Journal of Physics
To investigate the actual phenomena of transport on a complex network, we analyzed 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 analyzed the relationships between sales and sales of nearest neighborhoods from which we obtain a simple linear relationship between sales and the weighted sum of sales of nearest neighborhoods (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 outer-edge (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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Tokyo Institute of Technology
Hayafumi Watanabe, Hideki Takayasu, and Misako Takayasu