Layer entanglement in multiplex, temporal multiplex, and coupled multilayer networks

Complex networks, such as transportation networks, social networks, or biological networks, capture the complex system they model often by representing only one type of interactions. In real world systems, there may be many different aspects that connect entities together. These can be captured using multilayer networks, which combine different modalities of interactions in a single model. Coupling in multilayer networks may exhibit different properties which can be related to the very nature of the data they model (or to events in time-dependant data). We hypothesise that such properties may be reflected in the way layers are intertwined. In this paper, we investigated these through the prism of layer entanglement in coupled multilayer networks. We test over 30 real-life networks in 6 different disciplines (social, genetic, transport, co-authorship, trade, and neuronal networks). We further propose a random generator, displaying comparable patterns of elementary layer entanglement and transition coupling entanglement across 1,329,696 synthetic coupled multilayer networks. Our experiments demonstrate difference of layer entanglement across disciplines, and even suggest a link between entanglement intensity and homophily. We additionally study entanglement in 3 real world temporal datasets displaying a potential rise in entanglement activity prior to other network activity.