  A major problem in the study of complex socioeconomic systems is represented
by privacy issues$-$that can put severe limitations on the amount of accessible
information, forcing to build models on the basis of incomplete knowledge. In
this paper we investigate a novel method to reconstruct global topological
properties of a complex network starting from limited information. This method
uses the knowledge of an intrinsic property of the nodes (indicated as
fitness), and the number of connections of only a limited subset of nodes, in
order to generate an ensemble of exponential random graphs that are
representative of the real systems and that can be used to estimate its
topological properties. Here we focus in particular on reconstructing the most
basic properties that are commonly used to describe a network: density of
links, assortativity, clustering. We test the method on both benchmark
synthetic networks and real economic and financial systems, finding a
remarkable robustness with respect to the number of nodes used for calibration.
The method thus represents a valuable tool for gaining insights on
privacy-protected systems.
