Mesoscopic structures reveal the network between the layers of multiplex data sets

Multiplex networks describe a large variety of complex systems, whose elements (nodes) can be connected by different types of interactions forming different layers (networks) of the multiplex. Multiplex networks include social networks, transportation networks, or biological networks in the cell or in the brain. Extracting relevant information from these networks is of crucial importance for solving challenging inference problems and for characterizing the multiplex networks microscopic and mesoscopic structure. Here we propose an information theory method to extract the network between the layers of multiplex data sets, forming a network of networks. We build an indicator function, based on the entropy of network ensembles, to characterize the mesoscopic similarities between the layers of a multiplex network, and we use clustering techniques to characterize the communities present in this network of networks. We apply the proposed method to study the Multiplex Collaboration Network formed by scientists collaborating on different subjects and publishing in the American Physical Society journals. The analysis of this data set reveals the interplay between the collaboration networks and the organization of knowledge in physics.