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

Author

Watanabe, Hayafumi and Takayasu, Hideki and Takayasu, Misako

Abstract

To investigate the actual phenomenon 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 obtained a simple linear relationship between sales and the weighted sum of sales of nearest neighbourhoods (i.e. customers). In addition, we introduced 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) in proportion to the in-degree of destinations. From intensive numerical simulations, we found 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.