Zhai Xuemeng, Zhou Wanlei, Fei Gaolei, Liu Weiyi, Xu Zhoujun, Jiao Chengbo, Lu Cai, Hu Guangmin
School of Communication and Information Engineering, University of Electronic Science and Technology of China, Chengdu, China.
Faculty of Science, Engineering and Built Environment, Deakin University, 221 Burwood Highway, Burwood, VIC 3125, Australia.
Sci Rep. 2018 Feb 19;8(1):3245. doi: 10.1038/s41598-018-21286-0.
The multiple relationships among objects in complex systems can be described well by multiplex networks, which contain rich information of the connections between objects. The null model of networks, which can be used to quantify the specific nature of a network, is a powerful tool for analysing the structural characteristics of complex systems. However, the null model for multiplex networks remains largely unexplored. In this paper, we propose a null model for multiplex networks based on the node redundancy degree, which is a natural measure for describing the multiple relationships in multiplex networks. Based on this model, we define the modularity of multiplex networks to study the community structures in multiplex networks and demonstrate our theory in practice through community detection in four real-world networks. The results show that our model can reveal the community structures in multiplex networks and indicate that our null model is a useful approach for providing new insights into the specific nature of multiplex networks, which are difficult to quantify.
复杂系统中对象之间的多重关系可以通过多重网络很好地描述，多重网络包含对象之间连接的丰富信息。网络的零模型可用于量化网络的特定性质，是分析复杂系统结构特征的有力工具。然而，多重网络的零模型在很大程度上仍未被探索。在本文中，我们基于节点冗余度提出了一种多重网络的零模型，这是描述多重网络中多重关系的一种自然度量。基于该模型，我们定义了多重网络的模块化来研究多重网络中的社区结构，并通过在四个真实世界网络中的社区检测在实践中验证了我们的理论。结果表明，我们的模型可以揭示多重网络中的社区结构，并且表明我们的零模型是一种有用的方法，可为难以量化的多重网络的特定性质提供新的见解。
