Fitness-Dependent Topological Properties of the World Trade Web

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.

Figure 1

Cumulative fitness distribution (circles) of world countries and power law with slope $-1$ (solid line).

Figure 2

Comparison of the observed and expected dependence of the degree $k$ on the fitness $x$ (the circles are obtained through a logarithmic binning of raw data). The asymptotic trends $\tilde{k}=N-1$ and $\tilde{k}\approx \delta x$ are also shown.

Figure 3

Cumulative degree distributions $P_{>}(k)$: empirical (circles) and predicted (solid line). A power law with slope $-1.6$ is also shown (dashed line).

Figure 4

Average nearest neighbor degree $K^{nn}$ and clustering coefficient $C$ versus the degree $k$ for the real (circles) and model (solid line) webs.