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To investigate the actual phenomena of transport on a complex network, weanalysed empirical data for an inter-firm trading network, which consists ofabout one million Japanese firms and the sales of these firms (a salecorresponds to the total in-flow into a node). First, we analysed therelationships between sales and sales of nearest neighbourhoods from which weobtain a simple linear relationship between sales and the weighted sum of salesof nearest neighbourhoods (i.e., customers). In addition, we introduce a simplemoney transport model that is coherent with this empirical observation. In thismodel, a firm (i.e., customer) distributes money to its out-edges (suppliers)proportionally to the in-degree of destinations. From intensive numericalsimulations, we find that the steady flows derived from these models canapproximately reproduce the distribution of sales of actual firms. The sales ofindividual firms deduced from the money-transport model are shown to beproportional, on an average, to the real sales.

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