  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.
