Detangling the multilayer structure from an aggregated network

Multiplex interactions are common and essential in real-world systems. In many cases, we can only obtain aggregated networks without detailed information regarding the type of links contained within. Such single-layer networks oversimplify the structural information and lead to misunderstandings of some properties of real systems. In this context, network splitting which aims to correctly separate an aggregated network into multilayer networks, is a meaningful problem to address. To this end, we propose a simulated-annealing-like algorithm based on the link clustering coefficient. We verify the validity of this algorithm with several synthetic networks. Inter-similarities of layers are also taken into consideration, and we can find that the proposed method is valid even if there is a certain proportion of overlapping links between layers. Finally, we apply the algorithm to real international trading networks, which results in accurate splits of different layers.