  A fundamental problem in studying and modeling economic and financial systems
is represented by privacy issues, which put severe limitations on the amount of
accessible information. Here we introduce a novel, highly nontrivial method to
reconstruct the structural properties of complex weighted networks of this kind
using only partial information: the total number of nodes and links, and the
values of the strength for all nodes. The latter are used as fitness to
estimate the unknown node degrees through a standard configuration model. Then,
these estimated degrees and the strengths are used to calibrate an enhanced
configuration model in order to generate ensembles of networks intended to
represent the real system. The method, which is tested on real economic and
financial networks, while drastically reducing the amount of information needed
to infer network properties, turns out to be remarkably effective$-$thus
representing a valuable tool for gaining insights on privacy-protected
socioeconomic systems.
