Departament d'Enginyeria Informática i Matemátiques, Universitat Rovira I Virgili, Avda Paisos Catalans 26, Tarragona 43007, Spain.
School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, UK.
Nat Commun. 2015 Apr 23;6:6864. doi: 10.1038/ncomms7864.
Many complex systems can be represented as networks consisting of distinct types of interactions, which can be categorized as links belonging to different layers. For example, a good description of the full protein-protein interactome requires, for some organisms, up to seven distinct network layers, accounting for different genetic and physical interactions, each containing thousands of protein-protein relationships. A fundamental open question is then how many layers are indeed necessary to accurately represent the structure of a multilayered complex system. Here we introduce a method based on quantum theory to reduce the number of layers to a minimum while maximizing the distinguishability between the multilayer network and the corresponding aggregated graph. We validate our approach on synthetic benchmarks and we show that the number of informative layers in some real multilayer networks of protein-genetic interactions, social, economical and transportation systems can be reduced by up to 75%.
许多复杂系统可以表示为由不同类型相互作用组成的网络，这些相互作用可以归类为属于不同层的链接。例如，要完整描述全蛋白质-蛋白质相互作用组，对于某些生物体，需要多达七个不同的网络层，分别对应不同的遗传和物理相互作用，每个层包含数千个蛋白质-蛋白质关系。那么，一个基本的开放性问题是，实际上需要多少层才能准确地表示一个多层复杂系统的结构。在这里，我们引入了一种基于量子理论的方法，在最大限度地提高多层网络与相应聚合图之间可区分性的同时，将层数减少到最小。我们在合成基准上验证了我们的方法，并表明在一些真实的蛋白质-遗传相互作用、社会、经济和交通系统的多层网络中，信息丰富的层的数量可以减少多达 75%。
