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.

中文翻译：

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多路复用、时间多路复用和耦合多层网络中的层纠缠

复杂网络，例如交通网络、社交网络或生物网络，通常通过仅表示一种类型的交互来捕获它们建模的复杂系统。在现实世界的系统中，可能有许多不同的方面将实体连接在一起。这些可以使用多层网络来捕获，多层网络在单个模型中结合了不同的交互方式。多层网络中的耦合可能表现出不同的特性，这些特性可能与它们建模的数据的本质有关（或与时间相关数据中的事件）。我们假设这些属性可能反映在层交织的方式中。在本文中，我们通过耦合多层网络中的层纠缠棱镜来研究这些。我们测试了 6 个不同学科（社会、遗传、运输、合着、贸易和神经元网络）。我们进一步提出了一个随机发生器，在 1,329,696 个合成耦合多层网络中显示基本层纠缠和过渡耦合纠缠的可比模式。我们的实验证明了跨学科的层纠缠差异，甚至表明纠缠强度和同质性之间存在联系。我们还研究了 3 个真实世界时间数据集中的纠缠，显示纠缠活动在其他网络活动之前可能增加。甚至提出纠缠强度和同质性之间的联系。我们还研究了 3 个真实世界时间数据集中的纠缠，显示纠缠活动在其他网络活动之前可能增加。甚至提出纠缠强度和同质性之间的联系。我们还研究了 3 个现实世界时间数据集中的纠缠，显示纠缠活动在其他网络活动之前可能增加。