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.

Bankruptcy Prediction with Interfirm Network Structure

“…However, to consider the stability of an economy as a whole, we need to consider the effect from/on the interfirm trading network. The network structure in the economic system and its stability have been analyzed intensively in a recent study [10,11]. There have been articles on chain bankruptcy [12] or the robustness of the network structure [13], but the source of the network effect was limited to the destruction of nodes.…”

Extraction of conjugate main-stream structures from a complex network flow

“…Researchers of complex systems have reported the nonlinearity of local interactions [8][9][10][11] and investigated the flow for nontrivial network structures, where the basic equilibrium concept of detailed balance was no longer a natural assumption.…”

“…For example, human transport between nations [8] and cities [9,10], i.e., immigration and trafficking, are studied in the framework of general transport phenomena. Additionally, transactions between firms [11] and trades between nations are considered from the viewpoint ot money flow [24]. In particular, the trading network data of business firms are investigated intensively as typical real-world examples of scale-free networks; a node denotes a firm, and a directed link denotes the money flow from a buyer to a seller [7,11,[25][26][27].…”

“…Additionally, transactions between firms [11] and trades between nations are considered from the viewpoint ot money flow [24]. In particular, the trading network data of business firms are investigated intensively as typical real-world examples of scale-free networks; a node denotes a firm, and a directed link denotes the money flow from a buyer to a seller [7,11,[25][26][27]. Watanabe et al proposed a model for money transport on an interfirm trading network to explain empirical properties such as the power-law distribution of sales [7].…”

Simulation of Gross Domestic Product in International Trade Networks: Linear Gravity Transportation Model

“…The gravity transportation model (GTM) is known to be effective in examining a company's transaction networks [3,4]. The LGTM is a linearized form of the GTM and is a type of degree distribution model [5,6].…”