  A multiplex is a collection of network layers, each representing a specific
type of edges. This appears to be a genuine representation for many real-world
systems. However, due to a variety of potential factors, such as limited budget
and equipment, or physical impossibility, multiplex data can be difficult to
observe directly. Often, only partial information on the layer structure of the
system is available, whereas the remaining information is in the form of a
single-layer network. In this work, we face the problem of reconstructing the
hidden multiplex structure of an aggregated network from partial information.
We propose an algorithm that leverages the layer-wise community structure that
can be learned from partial observations to reconstruct the ground-truth
topology of the unobserved part of the multiplex. The algorithm is
characterized by a computational time that grows linearly with the network
size. We perform a systematic study of reconstruction problems for both
synthetic and real-world multiplex networks. We show that the ability of the
proposed method to solve the reconstruction problem is affected by the
heterogeneity of the individual layers and the similarity among the layers. On
real-world networks, we observe that the accuracy of the reconstruction
saturates quickly as the amount of available information increases. In genetic
interaction and scientific collaboration multiplexes for example, we find that
10% of ground-truth information yields 70% accuracy, while 30% information
allows for more than 90% accuracy.
