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A coarse graining algorithm based on m-order degree in complex network

Author

Listed:
  • Yang, Qing-Lin
  • Wang, Li-Fu
  • Zhao, Guo-Tao
  • Guo, Ge

Abstract

The coarse-grained technology of complex networks is a promising method to analyze large-scale networks. Coarse-grained networks are required to preserve some properties of the original networks. In this paper, we propose an m-order-degree-based coarse graining (MDCG) algorithm to keep some statistical properties and controllability of the original network by merging the nodes with the same or similar m-order degree. Compared with the previous coarse-grained algorithms, the proposed algorithm uses the m-order degree as the classification criterion, which not only requires less network information and smaller computation but also preserves more properties, especially to maintain controllability of the original network. Moreover, the proposed algorithm can control the size of the coarse-grained networks freely. The effectiveness of the proposed method is demonstrated by simulation analysis of some model networks and real networks.

Suggested Citation

  • Yang, Qing-Lin & Wang, Li-Fu & Zhao, Guo-Tao & Guo, Ge, 2020. "A coarse graining algorithm based on m-order degree in complex network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 558(C).
    • Handle: RePEc:eee:phsmap:v:558:y:2020:i:c:s0378437120304556
    DOI: 10.1016/j.physa.2020.124879
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    as
    1. Wang, Pei & Xu, Shuang, 2017. "Spectral coarse grained controllability of complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 478(C), pages 168-176.
    2. Yang-Yu Liu & Jean-Jacques Slotine & Albert-László Barabási, 2011. "Controllability of complex networks," Nature, Nature, vol. 473(7346), pages 167-173, May.
    3. Zhengzhong Yuan & Chen Zhao & Zengru Di & Wen-Xu Wang & Ying-Cheng Lai, 2013. "Exact controllability of complex networks," Nature Communications, Nature, vol. 4(1), pages 1-9, December.
    4. Chaoming Song & Shlomo Havlin & Hernán A. Makse, 2005. "Self-similarity of complex networks," Nature, Nature, vol. 433(7024), pages 392-395, January.
    5. Long, Yong-Shang & Jia, Zhen & Wang, Ying-Ying, 2018. "Coarse graining method based on generalized degree in complex network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 655-665.
    6. Hu, Sen & Yang, Hualei & Cai, Boliang & Yang, Chunxia, 2013. "Research on spatial economic structure for different economic sectors from a perspective of a complex network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(17), pages 3682-3697.
    7. Xu, Xiao-Ting & Wang, Nianxin & Bian, Jun & Zhou, Bin, 2019. "Understanding the diversity on power-law-like degree distribution in social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 576-581.
    8. C.-L. Tang & W.-X. Wang & X. Wu & B.-H. Wang, 2006. "Effects of average degree on cooperation in networked evolutionary game," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 53(3), pages 411-415, October.
    9. Wang, Minggang & Tian, Lixin, 2016. "From time series to complex networks: The phase space coarse graining," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 456-468.
    10. Deng, Yang & Jia, Zhen & Deng, Guangming & Zhang, Qiongfen, 2020. "Eigenvalue spectrum and synchronizability of multiplex chain networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    11. Sun, Xiaoqi & An, Haizhong & Liu, Xiaojia, 2018. "Network analysis of Chinese provincial economies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 1168-1180.
    12. Zhou, Bin & Xu, Xiao-Ting & Liu, Jian-Guo & Xu, Xiao-Ke & Wang, Nianxin, 2019. "Information interaction model for the mobile communication networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 1170-1176.
    13. Zhang, Hui & Zhuge, Chengxiang & Yu, Xiaohua, 2018. "Identifying hub stations and important lines of bus networks: A case study in Xiamen, China," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 394-402.
    14. Steven H. Strogatz, 2001. "Exploring complex networks," Nature, Nature, vol. 410(6825), pages 268-276, March.
    15. Feng, Xiangnan & Wei, Wei & Zhang, Renquan & Wang, Jiannan & Shi, Ying & Zheng, Zhiming, 2019. "Exploring the heterogeneity for node importance byvon Neumann entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 517(C), pages 53-65.
    16. Wang, Yang & Hu, Yanqing & Di, Zengru & Fan, Ying, 2011. "The effect of hub nodes on the community structure in scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(21), pages 4027-4033.
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    1. Serrano, Fernando E. & Ghosh, Dibakar, 2022. "Robust stabilization and synchronization in a network of chaotic systems with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).

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