replicate the purely binary topology very well [@Squartini_etal_2011a_pre], while the strength sequence is completely unable to replicate the weighted structure [@Squartini_etal_2011b_pre]. We aim at understanding whether the joint specification of strengths and degrees allows us to successfully replicate the weighted structure. To this end, we use exactly the same data set as refs. [@Squartini_etal_2011a_pre; @Squartini_etal_2011b_pre], so that consistent comparisons can be made. Such data set is described in sec. \[sec:data1\]. We also use a similar, but appropriately generalized, methodology. This is introduced in sec. \[sec:data2\].

   HS Code  Commodity                                                                                                                                     Value (USD)        Value per link (USD)   $\%$ of aggregate trade
  --------- ---------------------------------------------------------------------------------------------------------------------------------------- ---------------------- ---------------------- -------------------------
     84     Nuclear reactors, boilers, machinery and mechanical appliances; parts thereof                                                             $5.67\times 10^{11}$   $6.17\times 10^{7}$            11.37%
     85     Electric machinery, equipment and parts; sound equipment; television equipment                                                            $5.58\times 10^{11}$   $6.37\times 10^{7}$            11.18%
     27     Mineral fuels, mineral oils & products of their distillation; bitumin substances; mineral wax                                             $4.45\times 10^{11}$   $9.91\times 10^{7}$             8.92%
     87     Vehicles, (not railway, tramway, rolling stock); parts and accessories                                                                    $3.09\times 10^{11}$   $4.76\times 10^{7}$             6.19%
     90     Optical, photographic, cinematographic, measuring, checking, precision, medical or surgical instruments/apparatus; parts & accessories    $1.78\times 10^{11}$   $2.48\times 10^{7}$             3.58%
     39     Plastics and articles thereof.                                                                                                            $1.71\times 10^{11}$   $2.33\times 10^{7}$             3.44%
     29     Organic chemicals                                                                                                                         $1.67\times 