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See Refs. for exceptions. References also employ commodity-specific data to build a network view of economic development where one analyzes a tripartite graph, linking countries to the products they export and the capabilities needed to produce them. Unlike the present study, however, they do not explicitly consider the web of trade relations between any pair of countries.
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Since, as always happens in trade data, exports from country i to country j are reported twice (according to the reporting country-importer or exporter) and sometimes the two figures do not match, we follow Ref. and only employ import flows. For the sake of exposition, however, we follow the flow of goods and we treat imports from j to i as exports from i to j.
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A connected component of an undirected graph is a subgraph in which any two vertices are connected to each other by paths, and to which no more vertices or edges can be added while preserving its connectivity. That is, it is a maximal connected subgraph. In directed graphs, one must firstly define what it means for two nodes to be connected. We shall employ two different ways to define whether any two nodes in the binary directed graph are connected. According to the weaker one, any two nodes are connected if there is at least one directed link between the two. The stronger one assumes two nodes to be connected if there is a bilateral link between them.
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More precisely, the correlation coefficient between two node statistics related to the same commodity network c, i.e., Xc and Yc, is defined here as the product-moment (Pearson) sample correlation, i.e., i ( xic - xc ̄ ) ( yic - yc ̄ ) / [ (N-1 ) sXc sYc ], where xc ̄ and yc ̄ are sample averages and sXc and sYc are sample standard deviations across nodes in network c.
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Since correlations are symmetric, each figure actually reports-when convenient-correlations for two statistics, one in the upper-left triangle and the other in the lower-right triangle. Axes stand for HS codes.
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