can use the Lagrange multipliers $\vec{x}^*,\vec {y}^*$ to compute the expected value $\langle X \rangle$ of any (higher-order) network property $X(W)$: $$\label{avpr}
\langle X \rangle \equiv \sum_W X(W)P(W|\vec{x}^*,\vec{y}^*)$$ Comparing $\langle X \rangle$ with the observed value $X(W^*)$ allows us to verify whether the ‘reconstructed’ value of the property is indeed close to the empirical one.

We will also compare the predictions of the ECM with those of the WCM. The latter can be obtained by setting $\vec{x}=\vec{1}$ and maximizing the likelihood with respect to $\vec{y}$ alone, thus finding another vector $\vec{y}^{**}\ne\vec{y}^{*}$ [@mastrandrea2013enhanced].

A computationally fast and statistically unbiased algorithm to obtain the values of the Lagrange multipliers maximizing the likelihood of both the ECM and WCM (along with other maximum-entropy ensembles) has been recently introduced under the name of ‘Max & Sam’ (‘maximize and sample’) method [@mymaxsam]. We will use that algorithm in our analysis.

Results {#result}
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In this section, we first analyse in detail the aggregated trade network in the reference year 2002. Our choice of this particular snapshot is dictated by the need to compare our results with that of refs. [@Squartini_etal_2011b_pre; @Squartini_etal_2011a_pre], as we mentioned. We then consider the temporal evolution of the system. Finally, we 