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. By theoretical analysis, we obtain the mean-field solution of money-transport models and find thatthe scaling exponent can be determined from the  average degree of the nearest neighbours , which is one of the cardinal features of a network .
After 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 . Using theoretical analysis, we obtain the mean-field solution of money-transport models and find thatthe scaling exponent can be determined from the average degree of the nearest neighbours , which is one of the cardinal features of a network .