Reconstruction of Multiplex Networks with Correlated Layers

In many situations, the complete microscopic structure of a network is empirically inaccessible and has to be inferred from aggregate information using some probabilistic model. While several network reconstruction methods have been developed in the case of single-layer networks where nodes can be connected only by one type of link, the problem is still largely unexplored in the case of multiplex networks where several interdependent layers, each representing a distinct mode of connection, coexist. Even the most advanced network reconstruction techniques, when applied to each layer separately, may fail in replicating the inter-layer dependencies embodying the essence of multiplex networks. Here we develop a methodology to reconstruct a class of correlated multiplexes which includes, as a specific example that we study in detail, the multiplex network of international trade in different products. Our method starts from virtually any reconstruction model that successfully reproduces a set of desired marginal properties of each layer separately, i.e., node strengths and/or node degrees. It then introduces the minimal dependency structure required to replicate an additional set of higher-order properties, namely the portion of each node's degree and each node's strength that is shared and/or reciprocated across pairs of layers. These properties are found to provide empirically robust measures of inter-layer coupling, allowing for an accurate reconstruction of the world trade multiplex network. Our method allows for joint multi-layer connection probabilities to be reliably reconstructed from marginal ones, effectively bridging the gap between single-layer information and global multiplex properties.