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Network structure provides critical information for understanding the dynamic behavior of complex systems. However, the complete structure of real-world networks is often unavailable, thus it is crucially important to develop approaches to infer a more complete structure of networks. In this paper, we integrate the configuration model for generating random networks into an Expectation–Maximization–Aggregation (EMA) framework to reconstruct the complete structure of multiplex networks. We validate the proposed EMA framework against the Expectation–Maximization (EM) framework and random model on several real-world multiplex networks, including both covert and overt ones. It is found that the EMA framework generally achieves the best predictive accuracy compared to the EM framework and the random model. As the number of layers increases, the performance improvement of EMA over EM decreases. The inferred multiplex networks can be leveraged to inform the decision-making on monitoring covert networks as well as allocating limited resources for collecting additional information to improve reconstruction accuracy. For law enforcement agencies, the inferred complete network structure can be used to develop more effective strategies for covert network interdiction. 

Abstract 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.