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Degree Correlations in Two Layer Growth Model with Nonlinear Preferential Attachment Rule

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Theoretical Computer Science (NCTCS 2017)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 768))

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Abstract

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.

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Acknowledgment

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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Authors and Affiliations

  1. School of Computer Science and Technology, Guizhou University, Guiyang, China

    Youjun Lu & Daoyun Xu

  2. School of Mathematics and Statistics, Qiannan Normal University for Nationalities, Duyun, China

    Jincheng Zhou

Authors
  1. Youjun Lu
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  2. Daoyun Xu
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  3. Jincheng Zhou
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Corresponding author

Correspondence to Daoyun Xu .

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Editors and Affiliations

  1. The University of Texas at Dallas, Richardson, Texas, USA

    Dingzhu Du

  2. Hefei University of Technology, Hefei, Anhui Province, China

    Lian Li

  3. National University of Defense Technology, Changsha, Hunan, China

    En Zhu

  4. Huazhong University of Science and Technology, Wuhan, Hubei, China

    Kun He

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Lu, Y., Xu, D., Zhou, J. (2017). Degree Correlations in Two Layer Growth Model with Nonlinear Preferential Attachment Rule. In: Du, D., Li, L., Zhu, E., He, K. (eds) Theoretical Computer Science. NCTCS 2017. Communications in Computer and Information Science, vol 768. Springer, Singapore. https://doi.org/10.1007/978-981-10-6893-5_13

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  • DOI: https://doi.org/10.1007/978-981-10-6893-5_13

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  • Print ISBN: 978-981-10-6892-8

  • Online ISBN: 978-981-10-6893-5

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