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

Abstract

Complex networks, such as transportation networks, social networks, or biological networks, capture the complex system they model by often 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-dependent 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.

Feature-rich multiplex lexical networks reveal mental strategies of early language learning

“…We aim to further investigate the multiplex structure of the conformity core even through layers. To this aim, we leverage the concept of layer entanglement 47,48 , assessing how much the layers overlap and are balanced in the multiplex core against the whole multiplex structure. In detail, layer entanglement can be captured by two measures 47 : Entanglement intensity I, that computes how much layers overlap with other layers, and entanglement homogeneity H, that measures how much nodes are connected in a balanced way across layers.…”

“…To this aim, we leverage the concept of layer entanglement 47,48 , assessing how much the layers overlap and are balanced in the multiplex core against the whole multiplex structure. In detail, layer entanglement can be captured by two measures 47 : Entanglement intensity I, that computes how much layers overlap with other layers, and entanglement homogeneity H, that measures how much nodes are connected in a balanced way across layers. In the whole multiplex structure, we find that I tot = 0.09 and H tot = 0.83 , while in the conformity core/language kernel we find higher intensity and lower homogeneity values, I kernel = 0.29 and H kernel = 0.64 .…”

“…I partial_core = 0.39 and H partial_core = 0.77 . Moreover, layer entanglement can be computed on a temporal network as well 47 . By creating subgraphs of the original multiplex network with the first 200, 300 and 400 learned words, we registered values of H and I analogous to the ones of the full multiplex network.…”

Social Media Sensors for Weather-Caused Outage Prediction Based on Spatio–Temporal Multiplex Network Representation

“…An important property of a multiplex network is coupled edges (coupling E) which capture the transitions of the nodes between adjacent layers [18]. The network with the higher number of coupled edges tends to be more saturated and have richer connections compared to networks with low or noncoupled edges.…”