On the reconstruction limits of complex networks (2501.01437v2)

Abstract: Network reconstruction consists in retrieving the hidden interaction structure of a system from observations. Many reconstruction algorithms have been proposed, although less research has been devoted to describe their theoretical limitations. In this work, we adopt an information-theoretic perspective and define the reconstructability: The fraction of structural information recoverable from data. The reconstructability depends on the true data generating (TDG) model which is shown to set the reconstruction limit: any algorithm can perform, on average, at best like the TDG model. We show that the reconstructability is related to various performance measures, such as the probability of error and the Jaccard similarity. In an empirical context where the TDG model is unknown, we introduce the reconstruction index as an approximation of the reconstructability. We find that performing model selection is crucial for the validity of the reconstruction index as a proxy of the reconstructability of empirical time series and networks.