Fitness-Dependent Topological Properties of the World Trade Web

Abstract

Among the proposed network models, the hidden variable (or good get richer) one is particularly interesting, even if an explicit empirical test of its hypotheses has not yet been performed on a real network. Here we provide the first empirical test of this mechanism on the world trade web, the network defined by the trade relationships between world countries. We find that the power-law distributed gross domestic product can be successfully identified with the hidden variable (or fitness) determining the topology of the world trade web: all previously studied properties up to third-order correlation structure (degree distribution, degree correlations, and hierarchy) are found to be in excellent agreement with the predictions of the model. The choice of the connection probability is such that all realizations of the network with the same degree sequence are equiprobable.

International trade and financial integration: a weighted network analysis

“…have many partners)? We address this question by means of average nearest-neighbor degree (ANND) or strength (ANNS) (see Garlaschelli & Loffredo 2004. These coefficients measure for each node the average number (or weight) of neighbors of the neighbors of the node.…”

“…A number of recent papers has studied the topological properties of the International Trade Network (ITN), but has only relied on binary (unweighted) analysis (Serrano & Boguñá 2003, Garlaschelli & Loffredo 2004. This means that a link between any two countries in the network is either in place or not depending on whether the trade flow is greater than some given threshold.…”

“…In particular, the fact that the relation is decreasing suggests that highly interconnected countries tend to connect to poorly related ones in a hierarchical way. Garlaschelli & Loffredo (2004) aims at providing evidence in favor of so called hidden variable models whereby the topological properties of the network are determined by a single (fitness) variable, i.e. the potential ability of being connected.…”

“…Specifically the authors postulate that GDP plays this role in the case of the WTW. With respect to the distribution of the degree k (x) Garlaschelli & Loffredo (2004) claim that it is not a power law and therefore the WTW is not a scale-free network. On the other hand, they agree with Serrano & Boguñá (2003) in finding both disassortativity and that the clustering coefficient is decreasing in k, suggesting the presence of a hierarchical structure.…”

“…The correlation is lower in the case of trade than for finance and rather stable over time while different asset types do not display marked differences. The average nearest-neighbor degree (ANND) (see Garlaschelli & Loffredo 2004, DeMontis et al 2005) and the average nearest-neighbor strength (ANNS) allows one to assess the degree of assortativity that exists within the network. In other words, whether countries choose as partners nations with the same degree (strength) and whether the relationships with high/low degree countries (strength) follow the magnitude of the interaction.…”