the degrees of all countries, in contrast with the standard approach which considers the number of trade partners irrelevant.

Despite its fundamental role, the binary version of the WTW suffers from an important limitation: it ignores the magnitude of the observed trade relationships, thus giving only partial information about the network. Indeed, it turns out that the binary and weighted versions of the WTW are very different [@Fagiolo2008physa; @Fagiolo2009pre; @Fagiolo2010jeic]. For example, the edge weight and node strength distributions are highly left-skewed, indicating that few intense trade connections co-exist with a majority of low-intensity ones [@Bhatta2007a] and that countries with many partners are also the richest and most (globally) central. However, the latter trade very intensively with only few of their partners (which turn out to be themselves very connected), forming few but intensive trade clusters (i.e. triangular patterns) [@Fagiolo2009pre].

Recent works [@Squartini_etal_2011b_pre; @fagiolo2013null] have extended the binary null model analysis [@Squartini_etal_2011a_pre] to the weighted version of the WTW, now randomizing the latter while preserving each country’s (in- and out-)strength. This null model is known as the Weighted Configuration Model (WCM). Surprisingly, these studies found a very bad agreement between observed and expected higher-order weighted properties, mainly because the randomized 