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Network evolution by nonlinear preferential rewiring of edges

Author

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  • Xu, Xin-Jian
  • Hu, Xiao-Ming
  • Zhang, Li-Jie

Abstract

The mathematical framework for small-world networks proposed in a seminal paper by Watts and Strogatz sparked a widespread interest in modeling complex networks in the past decade. However, most of research contributing to static models is in contrast to real-world dynamic networks, such as social and biological networks, which are characterized by rearrangements of connections among agents. In this paper, we study dynamic networks evolved by nonlinear preferential rewiring of edges. The total numbers of vertices and edges of the network are conserved, but edges are continuously rewired according to the nonlinear preference. Assuming power-law kernels with exponents α and β, the network structures in stationary states display a distinct behavior, depending only on β. For β>1, the network is highly heterogeneous with the emergence of starlike structures. For β<1, the network is widely homogeneous with a typical connectivity. At β=1, the network is scale free with an exponential cutoff.

Suggested Citation

  • Xu, Xin-Jian & Hu, Xiao-Ming & Zhang, Li-Jie, 2011. "Network evolution by nonlinear preferential rewiring of edges," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(12), pages 2429-2434.
    • Handle: RePEc:eee:phsmap:v:390:y:2011:i:12:p:2429-2434
    DOI: 10.1016/j.physa.2011.02.032
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    Cited by:

    1. Zhong, Weicai & Liu, Jing, 2012. "Comments on “Scale-free networks without growth”," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(5), pages 2163-2165.
    2. Safaei, F. & Yeganloo, H. & Akbar, R., 2020. "Robustness on topology reconfiguration of complex networks: An entropic approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 170(C), pages 379-409.
    3. Yang, Xu-Hua & Lou, Shun-Li & Chen, Guang & Chen, Sheng-Yong & Huang, Wei, 2013. "Scale-free networks via attaching to random neighbors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(17), pages 3531-3536.
    4. Feng Su & Peijiang Yuan & Yuanwei Liu & Shuangqian Cao, 2018. "Network topology optimization by turning non-scale-free networks into scale-free networks using nonlinear preferential rewiring method," International Journal of Distributed Sensor Networks, , vol. 14(11), pages 15501477187, November.

    More about this item

    Keywords

    Complex networks; Rewiring networks;

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