Exploring multi-layer flow network of international trade based on flow distances

Based on the approach of flow distances, the international trade flow system is studied from the perspective of multi-layer flow network. A model of multi-layer flow network is proposed for modelling and analyzing multiple types of flows in flow systems. Then, flow distances are introduced, and symmetric minimum flow distance is presented. Subsequently, we discuss the establishment of the multi-layer flow networks of international trade from two coupled viewpoints, i.e., the viewpoint of commodity flow and that of money flow. Thus, the multi-layer flow networks of international trade is explored. First, trading "trophic levels" are adopted to depict positions that economies occupied in the flow network. We find that the distributions of trading "trophic levels" have the similar clustering pattern for different types of commodity, and there are some regularities between money flow network and commodity flow network. Second, we find that active and competitive countries trade a wide spectrum of products, while inactive and underdeveloped countries trade a limited variety of products. Besides, some abnormal countries import many types of goods, which the vast majority of countries do not need to import. It may indicate an abnormal economic status. Third, harmonic node centrality is proposed and we find the phenomenon of centrality stratification. It means that competitive countries tend to occupy the central positions in the trading of a large variety of commodities, while underdeveloped countries likely in the peripheral positions in the trading of their limited varieties of products. Fourth, we find that manufactured products have significant larger mean first-passage flow distances from the source to the sink than that of primary products.