Estimating topological properties of weighted networks from limited information

A problem typically encountered when studying complex systems is the limitedness of the informationavailable on their topology, which hinders our understanding of their structure and of the dynamical processestaking place on them. A paramount example is provided by financial networks, whose data are privacy protected:Banks publicly disclose only their aggregate exposure towards other banks, keeping individual exposures towardseach single bank secret. Yet, the estimation of systemic risk strongly depends on the detailed structure of theinterbank network. The resulting challenge is that of using aggregate information to statistically reconstruct anetwork and correctly predict its higher-order properties. Standard approaches either generate unrealisticallydense networks, or fail to reproduce the observed topology by assigning homogeneous link weights. Here, wedevelop a reconstruction method, based on statistical mechanics concepts, that makes use of the empirical linkdensity in a highly nontrivial way. Technically, our approach consists in the preliminary estimation of node degreesfrom empirical node strengths and link density, followed by a maximum-entropy inference based on a combinationof empirical strengths and estimated degrees. Our method is successfully tested on the international trade networkand the interbank money market, and represents a valuable tool for gaining insights on privacy-protected orpartially accessible systems.