IDEAS home Printed from https://ideas.repec.org/a/plo/pone00/0121946.html
   My bibliography  Save this article

Non-Homogeneous Fractal Hierarchical Weighted Networks

Author

Listed:
  • Yujuan Dong
  • Meifeng Dai
  • Dandan Ye

Abstract

A model of fractal hierarchical structures that share the property of non-homogeneous weighted networks is introduced. These networks can be completely and analytically characterized in terms of the involved parameters, i.e., the size of the original graph Nk and the non-homogeneous weight scaling factors r1, r2, · · · rM. We also study the average weighted shortest path (AWSP), the average degree and the average node strength, taking place on the non-homogeneous hierarchical weighted networks. Moreover the AWSP is scrupulously calculated. We show that the AWSP depends on the number of copies and the sum of all non-homogeneous weight scaling factors in the infinite network order limit.

Suggested Citation

  • Yujuan Dong & Meifeng Dai & Dandan Ye, 2015. "Non-Homogeneous Fractal Hierarchical Weighted Networks," PLOS ONE, Public Library of Science, vol. 10(4), pages 1-13, April.
    • Handle: RePEc:plo:pone00:0121946
    DOI: 10.1371/journal.pone.0121946
    as

    Download full text from publisher

    File URL: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0121946
    Download Restriction: no
    File URL: https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0121946&type=printable
    Download Restriction: no
    File URL: https://libkey.io/10.1371/journal.pone.0121946?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
    ---><---

    References listed on IDEAS

    as
    1. Carletti, Timoteo & Righi, Simone, 2010. "Weighted Fractal Networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(10), pages 2134-2142.
    2. 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.
    3. Zhongzhi Zhang & Shuigeng Zhou & Zhan Su & Tao Zou & Jihong Guan, 2008. "Random Sierpinski network with scale-free small-world and modular structure," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 65(1), pages 141-147, September.
    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. 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.
    2. 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.
    3. 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.
    4. Hu, Zhongren & Wu, Bo, 2023. "The average shortest distance of three colored substitution networks," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Dai, Meifeng & Wang, Xiaoqian & Sun, Yanqiu & Sun, Yu & Su, Weiyi, 2017. "Eigentime identities for random walks on a family of treelike networks and polymer networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 484(C), pages 132-140.
    10. Huang, Liang & Zheng, Yu, 2023. "Asymptotic formula on APL of fractal evolving networks generated by Durer Pentagon," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    11. Niu, Min & Song, Shuaishuai, 2018. "Scaling of average weighted shortest path and average receiving time on the weighted Cayley networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 707-717.
    12. 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.
    13. Wuyue (Phoebe) Shangguan & Alvin Chung Man Leung & Ashish Agarwal & Prabhudev Konana & Xi Chen, 2022. "Developing a Composite Measure to Represent Information Flows in Networks: Evidence from a Stock Market," Information Systems Research, INFORMS, vol. 33(2), pages 413-428, June.
    14. Dai, Meifeng & Dai, Changxi & Ju, Tingting & Shen, Junjie & Sun, Yu & Su, Weiyi, 2019. "Mean first-passage times for two biased walks on the weighted rose networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 268-278.
    15. Zeng, Cheng & Xue, Yumei & Huang, Yuke, 2021. "Fractal networks with Sturmian structure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 574(C).
    16. Chen, Jin & Le, Anbo & Wang, Qin & Xi, Lifeng, 2016. "A small-world and scale-free network generated by Sierpinski Pentagon," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 449(C), pages 126-135.
    17. 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).
    18. 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.
    19. Carletti, Timoteo & Righi, Simone, 2010. "Weighted Fractal Networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(10), pages 2134-2142.
    20. Wang, Songjing & Xi, Lifeng & Xu, Hui & Wang, Lihong, 2017. "Scale-free and small-world properties of Sierpinski networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 465(C), pages 690-700.

    More about this item

    Statistics

    Access and download statistics

    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:plo:pone00:0121946. 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: plosone (email available below). General contact details of provider: https://journals.plos.org/plosone/ .

    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.