Reconstruction of weighted networks via conditional entropy

Addressing the network reconstruction problem means facing the double challenge represented by the estimation of topology and the estimation of link weights. Among the methods proposed so far, some attribute weights to the binary configuration using a completely separate methodology, while others assume that the binary and weighted constraints jointly determine the final configuration in terms of both topology and weights.
Here we develop a theoretical framework that deals with the problem of link weight assignment rigorously, given the procedure adopted to reconstruct the binary topology. Our approach takes as input the available prior (probabilistic) information on the topological structure and subsequently derives the unbiased link weight assignment probability. The latter is determined by the maximization of the key quantity of our approach, i.e. the conditional entropy associated with link weights, given the topology.