Representing various networked data as multiplex networks, networks of networks and other multilayer networks can reveal completely new types of structures in these system. We introduce a general and principled graphlet framework for multilayer networks which allows one to break any multilayer network into small multilayered building blocks. These multilayer graphlets can be either analyzed themselves or used to do tasks such as comparing different systems. The method is flexible in terms of multilayer isomorphism, automorphism orbit definition, and the type of multilayer network. We illustrate our method for multiplex networks and show how it can be used to distinguish networks produced with multiple models from each other in an unsupervised way. In addition, we include an automatic way of generating the hundreds of dependency equations between the orbit counts needed to remove redundant orbit counts. The framework introduced here allows one to analyze multilayer networks with versatile semantics, and these methods can thus be used to analyze the structural building blocks of myriad multilayer networks.
翻译:作为多层网络、网络网络和其他多层网络代表各种网络数据,可以揭示这些系统中全新的结构类型。我们为多层网络引入了一个一般性和有原则的图形框架,允许一个人将任何多层网络破碎成小多层建筑块。这些多层石墨可以自己分析,也可以用来做诸如比较不同系统等任务。这种方法在多层地貌学、自动地貌轨道定义和多层网络类型方面是灵活的。我们展示了我们多层网络的方法,并展示了如何使用它来以不受监督的方式区分用多个模型生成的网络。此外,我们还包括了一种在清除冗余轨道计数所需的轨道计数之间生成数百个依赖方程式的自动方法。这里引入的框架允许一种分析多层网络,并使用多种多层网络的结构构造块。