in the WTW is steadily high [@Squartini_etal_2011a_pre; @Squartini_etal_2011b_pre; @Fagiolo2008physa], giving us reasonable confidence that we can focus on the temporal series of undirected networks. We therefore define the symmetric matrices $$\begin{aligned}
\tilde{w}_{ij}^{(c)}(t) &\equiv& \left\lfloor\frac{e_{ij}^{(c)}(t)+e_{ji}^{(c)}(t)}{2}\right\rceil,\notag\\ 
\tilde{w}_{ij}^{AGG}(t) &\equiv& \left\lfloor\frac{e_{ij}^{AGG}(t)+e_{ji}^{AGG}(t)}{2}\right\rceil \end{aligned}$$ where $\lfloor x \rceil$ represents the nearest integer to the nonnegative real number $x$ [^4]. The above matrices define an undirected weighted network where the weight of a link is the average of the trade flowing in either direction between two countries.

In order to wash away trend effects and make the data comparable over time, we normalized our weights according to the total trade volume for each year: $$w_{ij}^{(c)}(t)\equiv \frac{\tilde{w}_{ij}^{(c)}(t)}{\tilde{w}_{TOT}^{(c)}}, \qquad w_{ij}^{AGG}(t)\equiv \frac{\tilde{w}_{ij}^{AGG}(t)}{\tilde{w}_{TOT}^{AGG}}$$ where $\tilde{w}_{TOT}^{(c)}=\sum_{i=1}^N \sum_{j=i+1}^N \tilde{w}_{ij}^{(c)}$ and $\tilde{w}_{TOT}^{AGG}=\sum_{i=1}^N \sum_{j=i+1}^N \tilde{w}_{ij}^{AGG}$. In such a way, we end up with adimensional weights that allow proper comparisons over time and consistent analyses of the evolution of network properties.

The Enhanced Configuration Model\[sec:data2\]
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Our methodology makes intense use of the ECM [@mastrandrea2013enhanced], defined as an ensemble of weighted networks with given strengths and degrees. In some sense, the ECM unifies the BCM and the WCM, which have been separately used in previous analyses of the same data [@Squartini_etal_2011a_pre; @Squartini_etal_2011b_pre].

One can show [@Squartini_Garlaschelli_2011; 