Battiston Federico, Nicosia Vincenzo, Latora Vito
School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, United Kingdom.
School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, United Kingdom and Laboratorio sui Sistemi Complessi, Scuola Superiore di Catania, I-95123 Catania, Italy.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Mar;89(3):032804. doi: 10.1103/PhysRevE.89.032804. Epub 2014 Mar 12.
Many real-world complex systems consist of a set of elementary units connected by relationships of different kinds. All such systems are better described in terms of multiplex networks, where the links at each layer represent a different type of interaction between the same set of nodes rather than in terms of (single-layer) networks. In this paper we present a general framework to describe and study multiplex networks, whose links are either unweighted or weighted. In particular, we propose a series of measures to characterize the multiplexicity of the systems in terms of (i) basic node and link properties such as the node degree, and the edge overlap and reinforcement, (ii) local properties such as the clustering coefficient and the transitivity, and (iii) global properties related to the navigability of the multiplex across the different layers. The measures we introduce are validated on a genuinely multiplex data set of Indonesian terrorists, where information among 78 individuals are recorded with respect to mutual trust, common operations, exchanged communications, and business relationships.
许多现实世界中的复杂系统由一组通过各种关系相互连接的基本单元组成。所有这类系统用多重网络来描述更为合适，其中每一层的链接代表同一组节点之间不同类型的相互作用，而不是用（单层）网络来描述。在本文中，我们提出了一个描述和研究多重网络的通用框架，其链接可以是无权的或加权的。特别地，我们提出了一系列度量方法，从以下几个方面来刻画系统的多重性：（i）基本节点和链接属性，如节点度、边重叠和强化；（ii）局部属性，如聚类系数和传递性；（iii）与多重网络在不同层之间的可导航性相关的全局属性。我们引入的这些度量方法在一个关于印度尼西亚恐怖分子的真实多重数据集上得到了验证，该数据集中记录了78个人之间关于相互信任、共同行动、通信交流和商业关系的信息。
