Discrimination reveals reconstructability of multiplex networks from partial observations

An excellent method for predicting links in multiplex networks is reflected in its ability to reconstruct them accurately. Although link prediction methods perform well on estimating the existence probability of each potential link in monoplex networks by the set of partially observed links, we lack a mathematical tool to reconstruct the multiplex network from the observed aggregate topology and partially observed links in multiplex networks. Here, we fill this gap by developing a theoretical and computational framework that builds a probability space containing possible structures with a maximum likelihood estimation. Then, we discovered that the discrimination, an indicator quantifying differences between layers from an entropy perspective, determines the reconstructability, i.e., the accuracy of such reconstruction. This finding enables us to design the optimal strategy to allocate the set of observed links in different layers for promoting the optimal reconstruction of multiplex networks. Finally, the theoretical analyses are corroborated by empirical results from biological, social, engineered systems, and a large volume of synthetic networks. While the reconstruction of classic monolayer networks is a widely addressed problem, accurate reconstruction of multiplex networks is still an open challenge. Here the authors propose a statistical approach that allow to achieve optimal reconstruction of multiplex networks from partial observations and knowledge of the aggregated network.

Automated summary

This study introduces an excellent method for predicting links in multiplex networks, which can accurately reconstruct network structures based on partially observed links. The research reveals that discrimination is a key indicator affecting reconstruction accuracy, and proposes the optimal strategy to optimize the reconstruction of multiplex networks.