Abstract
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.
Highlights
Network science is a fundamental tool for modelling and analysing complex systems[1,2,3]
We use the set of adjacency matrixes representing each isolated network in a multiplex network to preserve the complete connection information of the multiplex network
Based on the null model of a single network, we introduce our null model with redundancy for multiplex networks (NMR): Definition 4
Summary
Network science is a fundamental tool for modelling and analysing complex systems[1,2,3]. Because network models capture the common features of complex systems, many network models have been proposed to study the modelling of real-world systems[11,12,13] These single-network models provide a general framework of systems from different fields such as social science[14], Internet topology[15], bioscience[16], engineering[17], economics[18], education[19], and so on. Each type of relationship among nodes can be described in each layer of the multiplex networks, and each network layer contains the same set of nodes Examples of such multiplex systems include social networks involving multiple relationships from different social platforms such as Twitter, YouTube and Facebook[40], epidemic networks with multiple diseases[41], and Internet topologies with multiple levels from the route level to the AS level[42]. A new measure is needed to replace the node degree in multiplex networks to constrain the null model of multiplex networks
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