IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v514y2019icp699-707.html
   My bibliography  Save this article

A new fractal reliability model for networks with node fractal growth and no-loop

Author

Listed:
  • Sun, Lina
  • Huang, Ning
  • Li, Ruiying
  • Bai, Yanan

Abstract

Evaluating the reliability of networked systems with existing exact or approximate methods often needs to characterize the detailed topology with node scale, which brings complexity and high computation effort. In this paper, a new reliability model based on the fractal unit with a bigger scale than nodes and a much smaller scale than whole network is proposed for networks with fractal growth and no-loop (NF-NL). The introduced model simplifies the K-terminal reliability (KTR) of a NF-NL network to a multiplication of different KTR of fractal units in the network. The corresponding algorithm is also given, which has a linear-time complexity O(V) when the fractal unit scale is very small. Compared with the existing models, the proposed model provides a novel way to construct the reliability model only dependent on two factors: (1) the fractal unit characteristics and (2) its iterative process. Finally, the widely investigated Koch network case is studied with the proposed model.

Suggested Citation

  • Sun, Lina & Huang, Ning & Li, Ruiying & Bai, Yanan, 2019. "A new fractal reliability model for networks with node fractal growth and no-loop," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 699-707.
    • Handle: RePEc:eee:phsmap:v:514:y:2019:i:c:p:699-707
    DOI: 10.1016/j.physa.2018.09.149
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437118312640
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2018.09.149?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. M. E. J. Newman & D. J. Watts, 1999. "Scaling and Percolation in the Small-World Network Model," Working Papers 99-05-034, Santa Fe Institute.
    2. Johansson, Jonas & Hassel, Henrik & Zio, Enrico, 2013. "Reliability and vulnerability analyses of critical infrastructures: Comparing two approaches in the context of power systems," Reliability Engineering and System Safety, Elsevier, vol. 120(C), pages 27-38.
    3. Zhongzhi Zhang & Shuigeng Zhou & Yi Qi & Jihong Guan, 2008. "Topologies and Laplacian spectra of a deterministic uniform recursive tree," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 63(4), pages 507-513, June.
    4. Ren, Hai-Peng & Song, Jihong & Yang, Rong & Baptista, Murilo S. & Grebogi, Celso, 2016. "Cascade failure analysis of power grid using new load distribution law and node removal rule," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 442(C), pages 239-251.
    5. Zhou, Jian & Huang, Ning & Coit, David W. & Felder, Frank A., 2018. "Combined effects of load dynamics and dependence clusters on cascading failures in network systems," Reliability Engineering and System Safety, Elsevier, vol. 170(C), pages 116-126.
    6. Zhang, Zhongzhi & Rong, Lili & Zhou, Shuigeng, 2007. "A general geometric growth model for pseudofractal scale-free web," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 377(1), pages 329-339.
    7. Carletti, Timoteo & Righi, Simone, 2010. "Weighted Fractal Networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(10), pages 2134-2142.
    8. L. Wang & F. Du & H. P. Dai & Y. X. Sun, 2006. "Random pseudofractal scale-free networks with small-world effect," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 53(3), pages 361-366, October.
    9. Chaoming Song & Shlomo Havlin & Hernán A. Makse, 2005. "Self-similarity of complex networks," Nature, Nature, vol. 433(7024), pages 392-395, January.
    10. Wang, Lei & Dai, Hua-ping & Sun, You-xian, 2007. "Random pseudofractal networks with competition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 383(2), pages 763-772.
    11. Kitsak, Maksim & Havlin, Shlomo & Paul, Gerald & Riccaboni, Massimo & Pammolli, Fabio & Stanley, H. Eugene, 2007. "Betweenness Centrality of Fractal and Non-Fractal Scale-Free Model Networks and Tests on Real Networks," MPRA Paper 15907, University Library of Munich, Germany.
    12. 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.
    13. 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.
    14. Lu, Zhe-Ming & Guo, Shi-Ze, 2012. "A small-world network derived from the deterministic uniform recursive tree," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(1), pages 87-92.
    15. Zhang, Yichao & Zhang, Zhongzhi & Zhou, Shuigeng & Guan, Jihong, 2010. "Deterministic weighted scale-free small-world networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(16), pages 3316-3324.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Huang, Da-Wen & Yu, Zu-Guo & Anh, Vo, 2017. "Multifractal analysis and topological properties of a new family of weighted Koch networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 695-705.
    2. Benatti, Alexandre & da F. Costa, Luciano, 2024. "On the transient and equilibrium features of growing fractal complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).
    3. Knor, Martin & Škrekovski, Riste, 2013. "Deterministic self-similar models of complex networks based on very symmetric graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(19), pages 4629-4637.
    4. Blagus, Neli & Šubelj, Lovro & Bajec, Marko, 2012. "Self-similar scaling of density in complex real-world networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(8), pages 2794-2802.
    5. Wei, Bo & Deng, Yong, 2019. "A cluster-growing dimension of complex networks: From the view of node closeness centrality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 522(C), pages 80-87.
    6. Wang, Jianrong & Wang, Jianping & Li, Lei & Yang, Bo, 2018. "A novel relay selection strategy based on deterministic small world model on CCN," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 559-568.
    7. Lu, Zhe-Ming & Guo, Shi-Ze, 2012. "A small-world network derived from the deterministic uniform recursive tree," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(1), pages 87-92.
    8. Le, Anbo & Gao, Fei & Xi, Lifeng & Yin, Shuhua, 2015. "Complex networks modeled on the Sierpinski gasket," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 646-657.
    9. Dai, Meifeng & Shao, Shuxiang & Su, Weiyi & Xi, Lifeng & Sun, Yanqiu, 2017. "The modified box dimension and average weighted receiving time of the weighted hierarchical graph," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 475(C), pages 46-58.
    10. Zeng, Cheng & Xue, Yumei & Huang, Yuke, 2021. "Fractal networks with Sturmian structure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 574(C).
    11. Dong, Gaogao & Tian, Lixin & Du, Ruijin & Fu, Min & Stanley, H. Eugene, 2014. "Analysis of percolation behaviors of clustered networks with partial support–dependence relations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 394(C), pages 370-378.
    12. 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.
    13. Zhang, Yue & Huang, Ning & Xing, Liudong, 2016. "A novel flux-fluctuation law for network with self-similar traffic," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 452(C), pages 299-310.
    14. 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.
    15. Ye, Dandan & Dai, Meifeng & Sun, Yu & Su, Weiyi, 2017. "Average weighted receiving time on the non-homogeneous double-weighted fractal networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 390-402.
    16. Zhou, Jian & Coit, David W. & Felder, Frank A. & Wang, Dali, 2021. "Resiliency-based restoration optimization for dependent network systems against cascading failures," Reliability Engineering and System Safety, Elsevier, vol. 207(C).
    17. Ma, Fei & Wang, Ping, 2024. "Understanding influence of fractal generative manner on structural properties of tree networks," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    18. Zong, Yue & Dai, Meifeng & Wang, Xiaoqian & He, Jiaojiao & Zou, Jiahui & Su, Weiyi, 2018. "Network coherence and eigentime identity on a family of weighted fractal networks," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 184-194.
    19. de Sá, Luiz Alberto Pereira & Zielinski, Kallil M.C. & Rodrigues, Érick Oliveira & Backes, André R. & Florindo, João B. & Casanova, Dalcimar, 2022. "A novel approach to estimated Boulingand-Minkowski fractal dimension from complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    20. Carletti, Timoteo & Righi, Simone, 2010. "Weighted Fractal Networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(10), pages 2134-2142.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:514:y:2019:i:c:p:699-707. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.