IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v449y2016icp126-135.html
   My bibliography  Save this article

A small-world and scale-free network generated by Sierpinski Pentagon

Author

Listed:
  • Chen, Jin
  • Le, Anbo
  • Wang, Qin
  • Xi, Lifeng

Abstract

The Sierpinski Pentagon is used to construct evolving networks, whose nodes are all solid regular pentagons in the construction of the Sierpinski Pentagon up to the stage t and any two nodes are neighbors if and only if the intersection of corresponding pentagons is non-empty and non-singleton. We show that such networks have the small-world and scale-free effects, but are not fractal scaling.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:449:y:2016:i:c:p:126-135
    DOI: 10.1016/j.physa.2015.12.089
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437115011176
    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.2015.12.089?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. Gallos, Lazaros K. & Song, Chaoming & Makse, Hernán A., 2007. "A review of fractality and self-similarity in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 386(2), pages 686-691.
    3. Réka Albert & Hawoong Jeong & Albert-László Barabási, 1999. "Diameter of the World-Wide Web," Nature, Nature, vol. 401(6749), pages 130-131, September.
    4. Réka Albert & Hawoong Jeong & Albert-László Barabási, 2000. "Error and attack tolerance of complex networks," Nature, Nature, vol. 406(6794), pages 378-382, July.
    5. 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.
    6. Chaoming Song & Shlomo Havlin & Hernán A. Makse, 2005. "Self-similarity of complex networks," Nature, Nature, vol. 433(7024), pages 392-395, January.
    7. 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.
    8. 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.
    9. H. Jeong & B. Tombor & R. Albert & Z. N. Oltvai & A.-L. Barabási, 2000. "The large-scale organization of metabolic networks," Nature, Nature, vol. 407(6804), pages 651-654, October.
    10. 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. 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.
    2. Pi, Xiaochen & Tang, Longkun & Chen, Xiangzhong, 2021. "A directed weighted scale-free network model with an adaptive evolution mechanism," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 572(C).
    3. Gao, Chao & Tang, Shaoting & Li, Weihua & Yang, Yaqian & Zheng, Zhiming, 2018. "Dynamical processes and epidemic threshold on nonlinear coupled multiplex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 330-338.
    4. 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.
    5. 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.
    6. Huang, Liang & Zheng, Yu, 2023. "Asymptotic formula on APL of fractal evolving networks generated by Durer Pentagon," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    7. 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.
    8. Fan, Jiaqi & Zhu, Jiali & Tian, Li & Wang, Qin, 2020. "Resistance Distance in Potting Networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).

    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. 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.
    2. Huang, Liang & Zheng, Yu, 2023. "Asymptotic formula on APL of fractal evolving networks generated by Durer Pentagon," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    3. Zeng, Cheng & Xue, Yumei & Huang, Yuke, 2021. "Fractal networks with Sturmian structure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 574(C).
    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. 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.
    6. Laurienti, Paul J. & Joyce, Karen E. & Telesford, Qawi K. & Burdette, Jonathan H. & Hayasaka, Satoru, 2011. "Universal fractal scaling of self-organized networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(20), pages 3608-3613.
    7. P.B., Divya & Lekha, Divya Sindhu & Johnson, T.P. & Balakrishnan, Kannan, 2022. "Vulnerability of link-weighted complex networks in central attacks and fallback strategy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 590(C).
    8. Yuji Yamamoto & Keiko Yokoyama, 2011. "Common and Unique Network Dynamics in Football Games," PLOS ONE, Public Library of Science, vol. 6(12), pages 1-6, December.
    9. Pagani, Giuliano Andrea & Aiello, Marco, 2013. "The Power Grid as a complex network: A survey," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(11), pages 2688-2700.
    10. Biggiero, Lucio & Angelini, Pier Paolo, 2015. "Hunting scale-free properties in R&D collaboration networks: Self-organization, power-law and policy issues in the European aerospace research area," Technological Forecasting and Social Change, Elsevier, vol. 94(C), pages 21-43.
    11. Gong, Pulin & van Leeuwen, Cees, 2003. "Emergence of scale-free network with chaotic units," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 321(3), pages 679-688.
    12. Guillaume, Jean-Loup & Latapy, Matthieu, 2006. "Bipartite graphs as models of complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 371(2), pages 795-813.
    13. Heath Henderson & Arnob Alam, 2022. "The structure of risk-sharing networks," Empirical Economics, Springer, vol. 62(2), pages 853-886, February.
    14. Dan Braha & Yaneer Bar-Yam, 2004. "Information Flow Structure in Large-Scale Product Development Organizational Networks," Industrial Organization 0407012, University Library of Munich, Germany.
    15. Wang, Li-Na & Wang, Kai & Shen, Jiang-Long, 2020. "Weighted complex networks in urban public transportation: Modeling and testing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    16. Dan Braha & Yaneer Bar-Yam, 2007. "The Statistical Mechanics of Complex Product Development: Empirical and Analytical Results," Management Science, INFORMS, vol. 53(7), pages 1127-1145, July.
    17. Ikeda, Nobutoshi, 2019. "Growth model for fractal scale-free networks generated by a random walk," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 424-434.
    18. Emmert-Streib, Frank & Dehmer, Matthias, 2009. "Fault tolerance of information processing in gene networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(4), pages 541-548.
    19. Chen, Qinghua & Shi, Dinghua, 2006. "Markov chains theory for scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 360(1), pages 121-133.
    20. Havlin, Shlomo & Stanley, H. Eugene & Bashan, Amir & Gao, Jianxi & Kenett, Dror Y., 2015. "Percolation of interdependent network of networks," Chaos, Solitons & Fractals, Elsevier, vol. 72(C), pages 4-19.

    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:449:y:2016:i:c:p:126-135. 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.