ESTIMATION OF FLUX BETWEEN INTERACTING NODES ON HUGE INTER-FIRM NETWORKS

Abstract

We analyze Japanese inter-firm network data showing scale-free properties as an example of a real complex network. The data contains information on money flow (annual transaction volume) between about 7000 pairs of firms. We focus on this money-flow data and investigate the correlation between various quantities such as sales or link numbers. We find that the flux from a buyer to a supplier is given by the product of the fractional powers of both sales with different exponents. This result indicates that the principle of detailed balance does not hold in the real transport of money; therefore, random walk type transport models such as PageRank are not suitable.