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Scaling of weighted spectral distribution in deterministic scale-free networks

Author

Listed:
  • Jiao, Bo
  • Nie, Yuan-ping
  • Shi, Jian-mai
  • Huang, Cheng-dong
  • Zhou, Ying
  • Du, Jing
  • Guo, Rong-hua
  • Tao, Ye-rong

Abstract

Scale-free networks are abundant in the real world. In this paper, we investigate the scaling properties of the weighted spectral distribution in several deterministic and stochastic models of evolving scale-free networks. First, we construct a new deterministic scale-free model whose node degrees have a unified format. Using graph structure features, we derive a precise formula for the spectral metric in this model. This formula verifies that the spectral metric grows sublinearly as network size (i.e., the number of nodes) grows. Additionally, the mathematical reasoning of the precise formula theoretically provides detailed explanations for this scaling property. Finally, we validate the scaling properties of the spectral metric using some stochastic models. The experimental results show that this scaling property can be retained regardless of local world, node deleting and assortativity adjustment.

Suggested Citation

  • Jiao, Bo & Nie, Yuan-ping & Shi, Jian-mai & Huang, Cheng-dong & Zhou, Ying & Du, Jing & Guo, Rong-hua & Tao, Ye-rong, 2016. "Scaling of weighted spectral distribution in deterministic scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 451(C), pages 632-645.
    • Handle: RePEc:eee:phsmap:v:451:y:2016:i:c:p:632-645
    DOI: 10.1016/j.physa.2016.01.096
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    References listed on IDEAS

    as
    1. Jia, Tao & Qin, Kun & Shan, Jie, 2014. "An exploratory analysis on the evolution of the US airport network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 413(C), pages 266-279.
    2. Deng, Ke & Zhao, Heping & Li, Dejun, 2007. "Effect of node deleting on network structure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 379(2), pages 714-726.
    3. Dai, Meifeng & Chen, Dandan & Dong, Yujuan & Liu, Jie, 2012. "Scaling of average receiving time and average weighted shortest path on weighted Koch networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(23), pages 6165-6173.
    4. J. Wu & M. Barahona & Y.-J. Tan & H.-Z. Deng, 2011. "Robustness of regular ring lattices based on natural connectivity," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(7), pages 1085-1092.
    5. Li, Xiang & Chen, Guanrong, 2003. "A local-world evolving network model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 328(1), pages 274-286.
    6. Sun, Yu & Dai, Meifeng & Xi, Lifeng, 2014. "Scaling of average weighted shortest path and average receiving time on weighted hierarchical networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 407(C), pages 110-118.
    7. Barabási, Albert-László & Ravasz, Erzsébet & Vicsek, Tamás, 2001. "Deterministic scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(3), pages 559-564.
    8. Chen, Mu & Yu, Boming & Xu, Peng & Chen, Jun, 2007. "A new deterministic complex network model with hierarchical structure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 385(2), pages 707-717.
    9. Colman, E.R. & Rodgers, G.J., 2014. "Local rewiring rules for evolving complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 416(C), pages 80-89.
    10. Xie, Zhou & Li, Xiang & Wang, Xiaofan, 2007. "A new community-based evolving network model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 384(2), pages 725-732.
    11. Lu, Zhe-Ming & Su, Yu-Xin & Guo, Shi-Ze, 2013. "Deterministic scale-free small-world networks of arbitrary order," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(17), pages 3555-3562.
    12. Yang-Yu Liu & Jean-Jacques Slotine & Albert-László Barabási, 2012. "Control Centrality and Hierarchical Structure in Complex Networks," PLOS ONE, Public Library of Science, vol. 7(9), pages 1-7, September.
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