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The topology of scale-free networks with an S-shaped nonlinear growth characteristic

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  • Dong, Xuefan
  • Liu, Yijung
  • Wu, Chao
  • Lian, Ying

Abstract

Calculations were conducted concerning the degree distribution functions of four models with an S-shaped growth characteristic and the preferential attachment rule, based on the mean field theory. Of these models, Model 1 displays the simplest sigmoid function, Model 2 and Model 3 are two extended models, and Model 4 depicts the law of population function. The results show that the graphs of the four degree distribution functions with their different gained control parameters are relatively similar to one another, thus, displaying a power-law form. In addition, a separated method was defined to calculate the degree distribution of single-peak, real-time networks with a symmetric or asymmetric characteristic. Such findings, to a large extent, will enrich the complex theory and could be conducive to understanding the evolutionary dynamics of S-shaped functions as well as other exponential functions.

Suggested Citation

  • Dong, Xuefan & Liu, Yijung & Wu, Chao & Lian, Ying, 2019. "The topology of scale-free networks with an S-shaped nonlinear growth characteristic," Chaos, Solitons & Fractals, Elsevier, vol. 121(C), pages 137-148.
  • Handle: RePEc:eee:chsofr:v:121:y:2019:i:c:p:137-148
    DOI: 10.1016/j.chaos.2019.02.007
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    References listed on IDEAS

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    1. Dessing, Maryke, 2002. "Labor supply, the family and poverty: the S-shaped labor supply curve," Journal of Economic Behavior & Organization, Elsevier, vol. 49(4), pages 433-458, December.
    2. Barabási, Albert-László & Albert, Réka & Jeong, Hawoong, 2000. "Scale-free characteristics of random networks: the topology of the world-wide web," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 281(1), pages 69-77.
    3. Kenneth Button & Jonathan Drexler, 2005. "Recovering Costs by Increasing Market Share: An Empirical Critique of the S-Curve," Journal of Transport Economics and Policy, University of Bath, vol. 39(3), pages 391-410, September.
    4. Jie Yan & Dimitris Assimakopoulos, 2009. "The small-world and scale-free structure of an internet technological community," International Journal of Information Technology and Management, Inderscience Enterprises Ltd, vol. 8(1), pages 33-49.
    5. Hao-Ming Du & Zi-You Gao & Zhi-Hong Zhu & Jian-Feng Zheng, 2014. "Impact of traffic demands on load distribution in congested scale-free networks," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 25(10), pages 1-12.
    6. Chunzhu Wei & Mark Padgham & Pablo Cabrera Barona & Thomas Blaschke, 2017. "Scale-Free Relationships between Social and Landscape Factors in Urban Systems," Sustainability, MDPI, vol. 9(1), pages 1-19, January.
    7. 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.
    8. Guida, Michele & Maria, Funaro, 2007. "Topology of the Italian airport network: A scale-free small-world network with a fractal structure?," Chaos, Solitons & Fractals, Elsevier, vol. 31(3), pages 527-536.
    9. Meilei Lv & Xinling Guo & Jiaquan Chen & Zhe-Ming Lu & Tingyuan Nie, 2015. "Second-order centrality correlation in scale-free networks," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 26(10), pages 1-10.
    10. Minjian Chen & Jing Ma & Yajie Hu & Fei Zhou & Jinxiu Li & Long Yan, 2015. "Is the S-shaped curve a general law? An application to evaluate the damage resulting from water-induced disasters," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 78(1), pages 497-515, August.
    11. Jie Yan & Dimitris Assimakopoulos, 2008. "The small-world and scale-free structure of an internet technological community," Post-Print hal-02313383, HAL.
    12. Dessing, Maryke, 2004. "Implications for minimum-wage policies of an S-shaped labor-supply curve," Journal of Economic Behavior & Organization, Elsevier, vol. 53(4), pages 543-568, April.
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    2. Dong, Xuefan & Lian, Ying, 2021. "A review of social media-based public opinion analyses: Challenges and recommendations," Technology in Society, Elsevier, vol. 67(C).

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