Mathematical Formulation of Multilayer Networks
Mathematical Formulation of Multilayer Networks
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DOI：
10.1103/physrevx.3.041022
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发表时间：
2013-12-04
影响因子：
12.5
通讯作者：
Arenas, Alex
中科院分区：
文献类型：
--
作者：
De Domenico, Manlio;Sole-Ribalta, Albert;Arenas, Alex
网络表示可用于描述各种复杂系统的结构。但是，大多数真实和工程系统都有多个子系统和连接性层，并且此类系统产生的数据非常丰富。深入了解此类系统需要概括“传统”网络理论，而新发现的数据现在可以测试越来越多的一般框架来研究网络。特别是，尽管邻接矩阵有助于描述传统的单层网络，但这种表示不足以分析和描述多重和时间依赖性网络。因此，必须开发一个更通用的数学框架，以应对多层复杂系统所带来的挑战。在本文中，我们介绍了一个张力框架来研究多层网络，并讨论了几个重要网络描述符和动态过程的概括，包括学位中心性，聚类系数，特征向量的中心性，模块化，模块化，von neumann entrypy和此框架，以下框架。 。我们研究了不同选择在构建这些概括中的影响，并说明了如何获得单层和多重网络的特殊情况的已知结果。我们的紧张方法将有助于解决多层复杂系统中的紧迫问题，例如推断谁在多渠道社交网络中影响谁（以及哪个媒体）以及为多模式运输系统开发路由技术。
A network representation is useful for describing the structure of a large variety of complex systems. However, most real and engineered systems have multiple subsystems and layers of connectivity, and the data produced by such systems are very rich. Achieving a deep understanding of such systems necessitates generalizing "traditional" network theory, and the newfound deluge of data now makes it possible to test increasingly general frameworks for the study of networks. In particular, although adjacency matrices are useful to describe traditional single-layer networks, such a representation is insufficient for the analysis and description of multiplex and time-dependent networks. One must therefore develop a more general mathematical framework to cope with the challenges posed by multilayer complex systems. In this paper, we introduce a tensorial framework to study multilayer networks, and we discuss the generalization of several important network descriptors and dynamical processes-including degree centrality, clustering coefficients, eigenvector centrality, modularity, von Neumann entropy, and diffusion-for this framework. We examine the impact of different choices in constructing these generalizations, and we illustrate how to obtain known results for the special cases of single-layer and multiplex networks. Our tensorial approach will be helpful for tackling pressing problems in multilayer complex systems, such as inferring who is influencing whom (and by which media) in multichannel social networks and developing routing techniques for multimodal transportation systems.