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The modeling of scale-free networks

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  • Chen, Qinghua
  • Shi, Dinghua

Abstract

In order to explore further the mechanism responsible for scale-free networks, we introduce two extended models of the BA model. The model A, where the system incorporates the addition of new links between existing nodes, a new node with new links and the rewiring of some links at every time step, all sites are born with some initial attractiveness. We calculate analytically the degree distribution. The system self-organizes into a scale-free network, the scaling exponent γ>2. The model B is a new model; we consider that some old links are deleted with the anti-preferential probability. The result indicates that the system evolves itself into a scale-free network, the scaling exponent γ varies from 2 to 3.

Suggested Citation

  • Chen, Qinghua & Shi, Dinghua, 2004. "The modeling of scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 335(1), pages 240-248.
    • Handle: RePEc:eee:phsmap:v:335:y:2004:i:1:p:240-248
    DOI: 10.1016/j.physa.2003.12.014
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    References listed on IDEAS

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    1. Steven H. Strogatz, 2001. "Exploring complex networks," Nature, Nature, vol. 410(6825), pages 268-276, March.
    2. Barabási, Albert-László & Albert, Réka & Jeong, Hawoong, 1999. "Mean-field theory for scale-free random networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 272(1), pages 173-187.
    3. Réka Albert & Hawoong Jeong & Albert-László Barabási, 1999. "Diameter of the World-Wide Web," Nature, Nature, vol. 401(6749), pages 130-131, September.
    4. H. Jeong & B. Tombor & R. Albert & Z. N. Oltvai & A.-L. Barabási, 2000. "The large-scale organization of metabolic networks," Nature, Nature, vol. 407(6804), pages 651-654, October.
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    Cited by:

    1. Wang, Jianrong & Wang, Jianping & Han, Dun, 2017. "Nonlinear dynamic evolution and control in CCFN with mixed attachment mechanisms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 466(C), pages 120-132.
    2. Kong, Joseph S. & Roychowdhury, Vwani P., 2008. "Preferential survival in models of complex ad hoc networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(13), pages 3335-3347.
    3. Geng, Xianmin & Li, Qiang, 2005. "Random models of scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 356(2), pages 554-562.
    4. Chen, Qinghua & Shi, Dinghua, 2006. "Markov chains theory for scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 360(1), pages 121-133.
    5. Wen, Guanghui & Duan, Zhisheng & Chen, Guanrong & Geng, Xianmin, 2011. "A weighted local-world evolving network model with aging nodes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(21), pages 4012-4026.
    6. Ma, Fei & Yao, Bing, 2017. "The relations between network-operation and topological-property in a scale-free and small-world network with community structure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 484(C), pages 182-193.

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