Weighted Configuration Model
  The configuration model is one of the most successful models for generating uncorrelated random networks. We analyze its behavior when the expected degree sequence follows a power law with exponent smaller than two. In this situation, the resulting network can be viewed as a weighted network with non trivial correlations between strength and degree. Our results are tested against large scale numerical simulations, finding excellent agreement. 
M. A. Serrano and M. Boguna