Degree Correlations in Two Layer Growth Model with Nonlinear Preferential Attachment Rule
Most real-world complex systems have multiple subsystems and layers of connectivity. All such systems can be described and represented in terms of multiplex network model, where the edges at each layer stand for the interactions of a different type between the same set of vertices. To better characterize and simulate such multiplex systems, we propose a new two layers network growth model based on nonlinear preferential attachment rule. Moreover, we obtain the joint degree distribution expression of the model via the rate equation approach at the steady state, and discuss the joint degree distribution and conditional average degree for the models of two different vertex weighted function, respectively. It was found that some existing multiplex network model is one of special cases of the model, and the corresponding joint degree distribution and the conditional average degree can also be obtained by the joint degree distribution expression of the model. Also, we observe that the conditional average degree expression is identical for the models of two different vertex weighted function. To verify our theoretical results, we perform Monte Carlo simulations for the models of two different vertex weighted function. Experiments indicate that our theoretical results are in accordance with the Monte Carlo simulation results well.
KeywordsMultiplex network model Nonlinear preferential attachment rule Joint degree distribution Conditional average degree
This work was supported by the National Natural Science Foundation of China (Grant Nos. 61262006, 61462001, 61540050, 61762019), the Major Applied Basic Research Program of Guizhou Province (Grant No. JZ20142001), and the Graduate Student Innovation Foundation of Guizhou University (Grant No. 2016047).
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