Before revision:  In this paper, we clarify the relationship between this non-trivial scaling and the structure of the network by applying mean-field approximation of  diffusion in a complex network to a money-transport model , which has been numerically shown to reproduce this empirical scaling.
After revision:  In a previous study using numerical simulations, we found that this scaling can be explained by both the money-transport model, where a firm (i.e. customer) distributes money to its out-edges (suppliers) in proportion to the in-degree of destinations, and by the correlations among the Japanese inter-firm trading network. However, in this previous study, we could not specifically identify what types of structure properties (or correlations) of the network determine the 1.3 exponent. In the present study, we more clearly elucidate the relationship between this non-trivial scaling and the structure of the network by applying mean-field approximation of diffusion in a complex network to a money-transport model , which has been numerically shown to reproduce this empirical scaling.