IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v392y2013i21p5461-5472.html
   My bibliography  Save this article

On the convergence rate of diffusion in the bidirectional Erdös–Rényi networks: An H2-norm perspective

Author

Listed:
  • Kashima, Kenji
  • Takahashi, Yutaka
  • Imura, Jun-ichi

Abstract

We investigate the convergence rates of diffusion in bidirectional Erdös–Rényi networks. We analytically and numerically demonstrate that the asymptotic distribution is far from a bell shape. Further, we numerically verify that the dynamical networks generated by the Barabasi–Albert model, which is a standard scale-free network model, exhibiting faster convergence of average consensus.

Suggested Citation

  • Kashima, Kenji & Takahashi, Yutaka & Imura, Jun-ichi, 2013. "On the convergence rate of diffusion in the bidirectional Erdös–Rényi networks: An H2-norm perspective," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(21), pages 5461-5472.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:21:p:5461-5472
    DOI: 10.1016/j.physa.2013.05.057
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437113005323
    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.2013.05.057?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. Steven H. Strogatz, 2001. "Exploring complex networks," Nature, Nature, vol. 410(6825), pages 268-276, March.
    2. Yang-Yu Liu & Jean-Jacques Slotine & Albert-László Barabási, 2011. "Controllability of complex networks," Nature, Nature, vol. 473(7346), pages 167-173, May.
    3. Réka Albert & Hawoong Jeong & Albert-László Barabási, 2000. "Error and attack tolerance of complex networks," Nature, Nature, vol. 406(6794), pages 378-382, July.
    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. Yang, Hyeonchae & Jung, Woo-Sung, 2016. "Structural efficiency to manipulate public research institution networks," Technological Forecasting and Social Change, Elsevier, vol. 110(C), pages 21-32.
    2. Li, Xin-Feng & Lu, Zhe-Ming, 2016. "Optimizing the controllability of arbitrary networks with genetic algorithm," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 447(C), pages 422-433.
    3. He, He & Yang, Bo & Hu, Xiaoming, 2016. "Exploring community structure in networks by consensus dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 342-353.
    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. Wouter Vermeer & Otto Koppius & Peter Vervest, 2018. "The Radiation-Transmission-Reception (RTR) model of propagation: Implications for the effectiveness of network interventions," PLOS ONE, Public Library of Science, vol. 13(12), pages 1-21, December.
    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. Prasanna Gai & Sujit Kapadia, 2011. "A Network Model of Super-Systemic Crises," Central Banking, Analysis, and Economic Policies Book Series, in: Rodrigo Alfaro (ed.),Financial Stability, Monetary Policy, and Central Banking, edition 1, volume 15, chapter 13, pages 411-432, Central Bank of Chile.
    8. Selen Onel & Abe Zeid & Sagar Kamarthi, 2011. "The structure and analysis of nanotechnology co-author and citation networks," Scientometrics, Springer;Akadémiai Kiadó, vol. 89(1), pages 119-138, October.
    9. Qingmin Hao & Jim Huangnan Shen & Chien-Chiang Lee, 2023. "Risk contagion of bank-firm loan network: evidence from China," Eurasian Business Review, Springer;Eurasia Business and Economics Society, vol. 13(2), pages 341-361, June.
    10. Jiang, Zhong-Yuan & Zeng, Yong & Liu, Zhi-Hong & Ma, Jian-Feng, 2019. "Identifying critical nodes’ group in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 121-132.
    11. Kashyap, G. & Ambika, G., 2019. "Link deletion in directed complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 631-643.
    12. Ding, Jie & Wen, Changyun & Li, Guoqi, 2017. "Key node selection in minimum-cost control of complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 251-261.
    13. Gordana Apic & Matthew J Betts & Robert B Russell, 2011. "Content Disputes in Wikipedia Reflect Geopolitical Instability," PLOS ONE, Public Library of Science, vol. 6(6), pages 1-5, June.
    14. Ying Duan & Xiuwen Fu & Wenfeng Li & Yu Zhang & Giancarlo Fortino, 2017. "Evolution of Scale-Free Wireless Sensor Networks with Feature of Small-World Networks," Complexity, Hindawi, vol. 2017, pages 1-15, July.
    15. Gao, Bo & Deng, Zhenghong & Zhao, Dawei, 2016. "Competing spreading processes and immunization in multiplex networks," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 175-181.
    16. Sun, Peng Gang & Che, Wanping & Quan, Yining & Wang, Shuzhen & Miao, Qiguang, 2022. "Random networks are heterogeneous exhibiting a multi-scaling law," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 587(C).
    17. Milena Oehlers & Benjamin Fabian, 2021. "Graph Metrics for Network Robustness—A Survey," Mathematics, MDPI, vol. 9(8), pages 1-48, April.
    18. Hu, Aihua & Cao, Jinde & Hu, Manfeng & Guo, Liuxiao, 2014. "Cluster synchronization in directed networks of non-identical systems with noises via random pinning control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 395(C), pages 537-548.
    19. Johan Rose Santos & Nur Diana Safitri & Maya Safira & Varun Varghese & Makoto Chikaraishi, 2021. "Road network vulnerability and city-level characteristics: A nationwide comparative analysis of Japanese cities," Environment and Planning B, , vol. 48(5), pages 1091-1107, June.
    20. Jianxi Gao & Xueming Liu & Daqing Li & Shlomo Havlin, 2015. "Recent Progress on the Resilience of Complex Networks," Energies, MDPI, vol. 8(10), pages 1-24, October.

    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:392:y:2013:i:21:p:5461-5472. 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.