IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v144y2021ics0960077921000989.html
   My bibliography  Save this article

Multifractal analysis of eigenvectors of small-world networks

Author

Listed:
  • Mishra, Ankit
  • Bandyopadhyay, Jayendra N.
  • Jalan, Sarika

Abstract

Many real-world complex systems have small-world topology characterized by the high clustering of nodes and short path lengths. It is well-known that higher clustering drives localization while shorter path length supports delocalization of the eigenvectors of networks. Using multifractals technique, we investigate localization properties of the eigenvectors of the adjacency matrices of small-world networks constructed using Watts-Strogatz algorithm. We find that the central part of the eigenvalue spectrum is characterized by strong multifractality whereas the tail part of the spectrum have Dq→ 1. Before the onset of the small-world transition, an increase in the random connections leads to an enhancement in the eigenvectors localization, whereas just after the onset, the eigenvectors show a gradual decrease in the localization. We have verified an existence of sharp change in the correlation dimension at the localization-delocalization transition.

Suggested Citation

  • Mishra, Ankit & Bandyopadhyay, Jayendra N. & Jalan, Sarika, 2021. "Multifractal analysis of eigenvectors of small-world networks," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    • Handle: RePEc:eee:chsofr:v:144:y:2021:i:c:s0960077921000989
    DOI: 10.1016/j.chaos.2021.110745
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921000989
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2021.110745?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. Oświe¸cimka, P. & Kwapień, J. & Drożdż, S., 2005. "Multifractality in the stock market: price increments versus waiting times," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 347(C), pages 626-638.
    2. Shang, Pengjian & Lu, Yongbo & Kamae, Santi, 2008. "Detecting long-range correlations of traffic time series with multifractal detrended fluctuation analysis," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 82-90.
    3. François Schmitt & Daniel Schertzer & Shaun Lovejoy, 1999. "Multifractal analysis of foreign exchange data," Applied Stochastic Models and Data Analysis, John Wiley & Sons, vol. 15(1), pages 29-53, March.
    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. He, Haoming & Xiao, Min & Lu, Yunxiang & Wang, Zhen & Tao, Binbin, 2023. "Control of tipping in a small-world network model via a novel dynamic delayed feedback scheme," Chaos, Solitons & Fractals, Elsevier, vol. 168(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. Li, Xing, 2021. "On the multifractal analysis of air quality index time series before and during COVID-19 partial lockdown: A case study of Shanghai, China," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).
    2. Zunino, Luciano & Figliola, Alejandra & Tabak, Benjamin M. & Pérez, Darío G. & Garavaglia, Mario & Rosso, Osvaldo A., 2009. "Multifractal structure in Latin-American market indices," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2331-2340.
    3. Zhou, Wei-Xing, 2012. "Finite-size effect and the components of multifractality in financial volatility," Chaos, Solitons & Fractals, Elsevier, vol. 45(2), pages 147-155.
    4. Pavón-Domínguez, P. & Serrano, S. & Jiménez-Hornero, F.J. & Jiménez-Hornero, J.E. & Gutiérrez de Ravé, E. & Ariza-Villaverde, A.B., 2013. "Multifractal detrended fluctuation analysis of sheep livestock prices in origin," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(19), pages 4466-4476.
    5. Zunino, L. & Tabak, B.M. & Figliola, A. & Pérez, D.G. & Garavaglia, M. & Rosso, O.A., 2008. "A multifractal approach for stock market inefficiency," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(26), pages 6558-6566.
    6. Liu, Hongzhi & Zhang, Xingchen & Zhang, Xie, 2020. "Multiscale multifractal analysis on air traffic flow time series: A single airport departure flight case," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    7. Xu, Kaiye & Shang, Pengjian & Feng, Guochen, 2015. "Multifractal time series analysis using the improved 0–1 test model," Chaos, Solitons & Fractals, Elsevier, vol. 70(C), pages 134-143.
    8. Wu, Yue & Shang, Pengjian & Chen, Shijian, 2019. "Modified multifractal large deviation spectrum based on CID for financial market system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1331-1342.
    9. Manimaran, P. & Narayana, A.C., 2018. "Multifractal detrended cross-correlation analysis on air pollutants of University of Hyderabad Campus, India," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 228-235.
    10. El Alaoui, Marwane & Benbachir, Saâd, 2013. "Multifractal detrended cross-correlation analysis in the MENA area," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(23), pages 5985-5993.
    11. Stanis{l}aw Dro.zd.z & Jaros{l}aw Kwapie'n & Marcin Wk{a}torek, 2023. "What is mature and what is still emerging in the cryptocurrency market?," Papers 2305.05751, arXiv.org.
    12. Guan, Sihai & Wan, Dongyu & Yang, Yanmiao & Biswal, Bharat, 2022. "Sources of multifractality of the brain rs-fMRI signal," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    13. Sornette, Didier & Zhou, Wei-Xing, 2006. "Importance of positive feedbacks and overconfidence in a self-fulfilling Ising model of financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(2), pages 704-726.
    14. Lux, Thomas & Morales-Arias, Leonardo & Sattarhoff, Cristina, 2011. "A Markov-switching multifractal approach to forecasting realized volatility," Kiel Working Papers 1737, Kiel Institute for the World Economy (IfW Kiel).
    15. Chen, Shu-Peng & He, Ling-Yun, 2010. "Multifractal spectrum analysis of nonlinear dynamical mechanisms in China’s agricultural futures markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(7), pages 1434-1444.
    16. Marcin Wątorek & Jarosław Kwapień & Stanisław Drożdż, 2022. "Multifractal Cross-Correlations of Bitcoin and Ether Trading Characteristics in the Post-COVID-19 Time," Future Internet, MDPI, vol. 14(7), pages 1-15, July.
    17. Jiang, Zhi-Qiang & Zhou, Wei-Xing, 2008. "Multifractal analysis of Chinese stock volatilities based on the partition function approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(19), pages 4881-4888.
    18. J. Doyne Farmer, 2000. "Physicists Attempt To Scale The Ivory Towers Of Finance," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(03), pages 311-333.
    19. Gao, Shilong & Gao, Nunan & Kan, Bixia & Wang, Huiqi, 2021. "Stochastic resonance in coupled star-networks with power-law heterogeneity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 580(C).
    20. Marcin Wk{a}torek & Stanis{l}aw Dro.zd.z & Jaros{l}aw Kwapie'n & Ludovico Minati & Pawe{l} O'swik{e}cimka & Marek Stanuszek, 2020. "Multiscale characteristics of the emerging global cryptocurrency market," Papers 2010.15403, arXiv.org, revised Mar 2021.

    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:chsofr:v:144:y:2021:i:c:s0960077921000989. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.