Mean field approximation for biased diffusion on Japanese inter-firm trading network

Area of Science:

• Economics
• Network Science
• Complexity Science

Background:

• A nonlinear power law (exponent 1.3) was observed between the number of business partners and sales for Japanese firms.
• Previous studies suggested a money-transport model and network correlations explain this scaling, but network structure's role was unclear.

Purpose of the Study:

• To elucidate the relationship between nonlinear scaling and network structure in inter-firm trading networks.
• To identify specific network properties determining the observed scaling exponent.

Main Methods:

• Application of mean-field approximation of diffusion in complex networks to the money-transport model.
• Theoretical analysis to derive the mean-field solution of the model.

Main Results:

• The study found that the scaling exponent of 1.3 is determined by the power law of the average degree of nearest neighbors.
• This relationship has an exponent of -0.7 for the Japanese firms analyzed.

Conclusions:

• The network structure, specifically the average degree of nearest neighbors, is a key determinant of the observed nonlinear scaling between business partners and sales.
• Mean-field approximation provides a theoretical framework to understand this phenomenon in complex economic networks.