IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v436y2015icp646-657.html
   My bibliography  Save this article

Complex networks modeled on the Sierpinski gasket

Author

Listed:
  • Le, Anbo
  • Gao, Fei
  • Xi, Lifeng
  • Yin, Shuhua

Abstract

In this paper, we use the Sierpinski gasket to construct evolving networks Gt whose node set is the solid regular triangles in the construction of the Sierpinski gasket up to the stage t and any two nodes are neighbors if and only if the corresponding solid triangles are in contact with each other on boundary. Using the encoding method, we show that our evolving networks are scale-free (power-law degree distribution) and have the small-world effect (small average path length and high clustering coefficient).

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:436:y:2015:i:c:p:646-657
    DOI: 10.1016/j.physa.2015.05.048
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037843711500463X
    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.2015.05.048?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. Guan, Jihong & Wu, Yuewen & Zhang, Zhongzhi & Zhou, Shuigeng & Wu, Yonghui, 2009. "A unified model for Sierpinski networks with scale-free scaling and small-world effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(12), pages 2571-2578.
    2. Chen, Renxia & Fu, Xinchu & Wu, Qingchu, 2012. "On topological properties of the octahedral Koch network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 880-886.
    3. Carletti, Timoteo & Righi, Simone, 2010. "Weighted Fractal Networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(10), pages 2134-2142.
    4. 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.
    5. Tomaso Aste & Ruggero Gramatica & T. Di Matteo, 2011. "Exploring complex networks via topological embedding on surfaces," Papers 1107.3456, arXiv.org, revised Aug 2012.
    6. Chaoming Song & Shlomo Havlin & Hernán A. Makse, 2005. "Self-similarity of complex networks," Nature, Nature, vol. 433(7024), pages 392-395, January.
    7. S. Condamin & O. Bénichou & V. Tejedor & R. Voituriez & J. Klafter, 2007. "First-passage times in complex scale-invariant media," Nature, Nature, vol. 450(7166), pages 77-80, November.
    8. 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)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Wen, Tao & Jiang, Wen, 2018. "An information dimension of weighted complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 501(C), pages 388-399.
    2. Park, Alex & Lappas, Petros, 2017. "Evaluating demand charge reduction for commercial-scale solar PV coupled with battery storage," Renewable Energy, Elsevier, vol. 108(C), pages 523-532.
    3. Gros, Daniel & De Groen, Willem Pieter, 2015. "Will the Single Resolution Fund be a �baby tiger� during the transition?," CEPS Papers 11192, Centre for European Policy Studies.
    4. 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.
    5. Huang, Liang & Zheng, Yu, 2023. "Asymptotic formula on APL of fractal evolving networks generated by Durer Pentagon," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    6. Zeng, Cheng & Xue, Yumei & Huang, Yuke, 2021. "Fractal networks with Sturmian structure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 574(C).
    7. 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.
    8. Köberle, Alexandre C. & Garaffa, Rafael & Cunha, Bruno S.L. & Rochedo, Pedro & Lucena, André F.P. & Szklo, Alexandre & Schaeffer, Roberto, 2018. "Are conventional energy megaprojects competitive? Suboptimal decisions related to cost overruns in Brazil," Energy Policy, Elsevier, vol. 122(C), pages 689-700.
    9. 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.

    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, Liang & Zheng, Yu, 2023. "Asymptotic formula on APL of fractal evolving networks generated by Durer Pentagon," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    2. 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.
    3. 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.
    4. Zeng, Cheng & Xue, Yumei & Huang, Yuke, 2021. "Fractal networks with Sturmian structure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 574(C).
    5. 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.
    6. Carletti, Timoteo & Righi, Simone, 2010. "Weighted Fractal Networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(10), pages 2134-2142.
    7. 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.
    8. He, Jia & Xue, Yumei, 2018. "Scale-free and small-world properties of hollow cube networks," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 11-15.
    9. 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).
    10. 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.
    11. Wijesundera, Isuri & Halgamuge, Malka N. & Nirmalathas, Ampalavanapillai & Nanayakkara, Thrishantha, 2016. "MFPT calculation for random walks in inhomogeneous networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 986-1002.
    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. 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.
    14. 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.
    15. Yao, Jialing & Sun, Bingbin & Xi, lifeng, 2019. "Fractality of evolving self-similar networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 211-216.
    16. Duan, Shuyu & Wen, Tao & Jiang, Wen, 2019. "A new information dimension of complex network based on Rényi entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 516(C), pages 529-542.
    17. Ikeda, Nobutoshi, 2020. "Fractal networks induced by movements of random walkers on a tree graph," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    18. Khajehnejad, Moein, 2019. "Efficiency of long-range navigation on Treelike fractals," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 102-110.
    19. Sun, Bingbin & Yao, Jialing & Xi, Lifeng, 2019. "Eigentime identities of fractal sailboat networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 520(C), pages 338-349.
    20. Lu, Qing-Chang & Xu, Peng-Cheng & Zhao, Xiangmo & Zhang, Lei & Li, Xiaoling & Cui, Xin, 2022. "Measuring network interdependency between dependent networks: A supply-demand-based approach," Reliability Engineering and System Safety, Elsevier, vol. 225(C).

    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:436:y:2015:i:c:p:646-657. 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.