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We propose a model of concurrent three-state spreading dynamics on multiplex networks to study the co-evolution process of epidemic spreading and information diffusion. The spreading dynamics and information diffusion process are both described by three-state models which can be used to address a wide range of common spreading behaviors. As accurate prediction is important in understanding the behaviors of complicated spreading dynamics, based on our proposed model, we develop a continuous-time effective degree theory (EDT) to delicately analyze the concurrent dynamics. We show that compared to the Monte Carlo simulations, this developed theory could predict the behavior of the dynamics in high accuracy, outperforming the dominantly adopted heterogeneous mean field theory applied on relevant dynamics on multiplex networks.

Multiplex networks, where nodes may interact through several different types of links, have been used widely to describe various complex systems. Many complex systems have an important feature that pairs of nodes may be connected by different types of links at the same time. In order to study the effect of the overlapped links systematically, in this paper I propose an algorithm to generate general multiplex networks with overlapped links. This algorithm could construct multiplex networks with arbitrary degree–degree distribution in each layer, and more importantly, could further adjust the proportion of overlapped links over a wide range. Therefore, the algorithm proposed in this paper offers an approach to construct multiplex networks into a delicate extent, which may provide a formal setting to study the topological impact of multiplex networks in a systematic manner.

Multiplex networks have been used to describe multilevel system by the way of combining several layers of sub-networks with one layer representing one sub-level system. Many multiplexes are characterized by a significant shared links in different layers. For this new network framework, research efforts have been paid on the study of its topological and dynamical properties. However, in these studies the network structures are mostly simple or specific, and the shared links in different layers has been mostly neglected, despite the fact that it is an ubiquitous phenomenon in most multiplexes. To systemically study multiplex network, a general multiplex network framework is necessary. In this work, we introduce an algorithm to generate a multiplex networks with shared links whose degree correlation functions of all its layers, the nodal degree correlation function between the layers, and the size of the resulting network are all tunable. Moreover, we give an upper bound of the average degree of the resulting network when the degree correlation functions introduced above are given and make efforts to maximize the average nodal degree of the multiplex networks. This algorithm may serve as a good candidate of standard technique for multiplex network generation.

Epidemic spreading processes on top of multiplex networks have more dynamical properties than on single layered networks. To describe the intertwined processes on such networks, heterogeneous mean field approach (HMF) have been proposed for the continuous-time processes. However, it has been shown that the time evolution of infected individuals and the final epidemic size obtained from this approach have remarkable discrepancy with those from the Monte Carlo simulations. In this paper, we extend effective degree theory (EDT) for analyzing continuous-time epidemic processes on multiplex networks based on SIR epidemic model. Predictions obtained from the theory are shown to have excellent agreement with Monte Carlo simulations.

Multiplex networks have been used to describe multilevel system by the way of combining several layers of sub-networks with one layer representing one sub-level system. For this new network framework, research efforts have been paid on the study of its topological and dynamical properties. However, in these studies the network structures are mostly simple or specific. To systemically study multiplex network, a general multiplex network framework is necessary. In this work, we introduce an algorithm by which we could generate a multiplex network whose degree correlation functions of all its layers, the nodal degree correlation function between the layers, and the size of the resulting network are all tunable. Moreover, we give an upper bound of the average degree of the resulting network when the degree correlation functions introduced above are given. This algorithm may serve as a good candidate of standard technique for multiplex network generation.

There is growing interest in multiplex networks where individual nodes take part in several layers of networks simultaneously. From transportation networks to complex infrastructures, and to social and communication networks, a large variety of systems can be described in terms of multiplexes formed by a set of nodes interacting through different layers of networks, for example, in social networks where each individual node has different kinds of social ties or transportation systems where each location is connected to another location by different types of transport. Many of these multiplexes are characterized by a significant overlap of the links in different layers. However, so far the overlap of the links in different layers has been mostly neglected, despite the fact that it is an ubiquitous phenomenon in most multiplexes. In this paper we introduce a general algorithm to generate a multiplex networks with overlapped links. In this approach, we make efforts to maximize the average nodal degree of the multiplex networks. We hope the algorithm will shed light on the multiplex networks generations.