IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v580y2021ics0378437121004313.html
   My bibliography  Save this article

Network navigation with non-Lèvy superdiffusive random walks

Author

Listed:
  • Fuentes, Emilio Aced
  • Santini, Simone

Abstract

We introduce a formalism based on a continuous time approximation to study the characteristics of random walks with jumps to random locations of the networks (Pagerank random walks). We find that the diffusion of the occupancy probability has a dynamics that exponentially “forgets” the initial conditions and settles to a steady state that depends only on the characteristics of the network. In the special case in which the walk begins from a single node, we show that the largest eigenvalue of the transition value (λ1=1) does not contribute to the dynamic and that the probability is constant in the direction of the corresponding eigenvector. We study the process of visiting new nodes, which we find to have a dynamic similar to that of the occupancy probability. Finally, we determine the average transit time between nodes 〈T〉.

Suggested Citation

  • Fuentes, Emilio Aced & Santini, Simone, 2021. "Network navigation with non-Lèvy superdiffusive random walks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 580(C).
  • Handle: RePEc:eee:phsmap:v:580:y:2021:i:c:s0378437121004313
    DOI: 10.1016/j.physa.2021.126158
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437121004313
    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.2021.126158?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. Lebensztayn, E. & Rodriguez, P.M., 2013. "A connection between a system of random walks and rumor transmission," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(23), pages 5793-5800.
    2. de Guzzi Bagnato, Guilherme & Ronqui, José Ricardo Furlan & Travieso, Gonzalo, 2018. "Community detection in networks using self-avoiding random walks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 1046-1055.
    3. A. Tabrizi, Shayan & Shakery, Azadeh & Asadpour, Masoud & Abbasi, Maziar & Tavallaie, Mohammad Ali, 2013. "Personalized PageRank Clustering: A graph clustering algorithm based on random walks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(22), pages 5772-5785.
    4. Xu, Xiao-Ke & Zhu, Jonathan J.H., 2016. "Flexible sampling large-scale social networks by self-adjustable random walk," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 463(C), pages 356-365.
    5. Marta C. González & César A. Hidalgo & Albert-László Barabási, 2009. "Understanding individual human mobility patterns," Nature, Nature, vol. 458(7235), pages 238-238, March.
    6. Sen, Parongama, 2019. "Unusual scaling in a discrete quantum walk with random long range steps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 266-273.
    7. D. Brockmann & L. Hufnagel & T. Geisel, 2006. "The scaling laws of human travel," Nature, Nature, vol. 439(7075), pages 462-465, January.
    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. Maxime Lenormand & Miguel Picornell & Oliva G Cantú-Ros & Antònia Tugores & Thomas Louail & Ricardo Herranz & Marc Barthelemy & Enrique Frías-Martínez & José J Ramasco, 2014. "Cross-Checking Different Sources of Mobility Information," PLOS ONE, Public Library of Science, vol. 9(8), pages 1-10, August.
    2. Huang, Feihu & Qiao, Shaojie & Peng, Jian & Guo, Bing & Xiong, Xi & Han, Nan, 2019. "A movement model for air passengers based on trip purpose," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 798-808.
    3. Shanshan Wan & Zhuo Chen & Cheng Lyu & Ruofan Li & Yuntao Yue & Ying Liu, 2022. "Research on disaster information dissemination based on social sensor networks," International Journal of Distributed Sensor Networks, , vol. 18(3), pages 15501329221, March.
    4. Chaogui Kang & Yu Liu & Diansheng Guo & Kun Qin, 2015. "A Generalized Radiation Model for Human Mobility: Spatial Scale, Searching Direction and Trip Constraint," PLOS ONE, Public Library of Science, vol. 10(11), pages 1-11, November.
    5. Li, Ze-Tao & Nie, Wei-Peng & Cai, Shi-Min & Zhao, Zhi-Dan & Zhou, Tao, 2023. "Exploring the topological characteristics of urban trip networks based on taxi trajectory data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 609(C).
    6. Cai, Hua & Zhan, Xiaowei & Zhu, Ji & Jia, Xiaoping & Chiu, Anthony S.F. & Xu, Ming, 2016. "Understanding taxi travel patterns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 457(C), pages 590-597.
    7. Toru Nakamura & Toru Takumi & Atsuko Takano & Fumiyuki Hatanaka & Yoshiharu Yamamoto, 2013. "Characterization and Modeling of Intermittent Locomotor Dynamics in Clock Gene-Deficient Mice," PLOS ONE, Public Library of Science, vol. 8(3), pages 1-8, March.
    8. Chen, Roger B., 2018. "Models of count with endogenous choices," Transportation Research Part B: Methodological, Elsevier, vol. 117(PB), pages 862-875.
    9. Barmak, D.H. & Dorso, C.O. & Otero, M., 2016. "Modelling dengue epidemic spreading with human mobility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 447(C), pages 129-140.
    10. Nie, Wei-Peng & Cai, Shi-Min & Zhao, Zhi-Dan & Zhou, Tao, 2022. "Revealing mobility pattern of taxi movements with its travel trajectory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 598(C).
    11. Christensen, Claire & Albert, István & Grenfell, Bryan & Albert, Réka, 2010. "Disease dynamics in a dynamic social network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(13), pages 2663-2674.
    12. Dong, Bing & Liu, Yapan & Fontenot, Hannah & Ouf, Mohamed & Osman, Mohamed & Chong, Adrian & Qin, Shuxu & Salim, Flora & Xue, Hao & Yan, Da & Jin, Yuan & Han, Mengjie & Zhang, Xingxing & Azar, Elie & , 2021. "Occupant behavior modeling methods for resilient building design, operation and policy at urban scale: A review," Applied Energy, Elsevier, vol. 293(C).
    13. Li, Jun & Fu, Siyao & He, Haibo & Jia, Hongfei & Li, Yanzhong & Guo, Yi, 2015. "Simulating large-scale pedestrian movement using CA and event driven model: Methodology and case study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 437(C), pages 304-321.
    14. Qianqian Liu & Qun Wang, 2017. "A comparative study on uncooperative search models in survivor search and rescue," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 89(2), pages 843-857, November.
    15. Li, Yan & Ye, Hang & Zhang, Hong, 2016. "Evolution of cooperation driven by social-welfare-based migration," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 445(C), pages 48-56.
    16. Tini Garske & Hongjie Yu & Zhibin Peng & Min Ye & Hang Zhou & Xiaowen Cheng & Jiabing Wu & Neil Ferguson, 2011. "Travel Patterns in China," PLOS ONE, Public Library of Science, vol. 6(2), pages 1-9, February.
    17. Saberi, Meead & Ghamami, Mehrnaz & Gu, Yi & Shojaei, Mohammad Hossein (Sam) & Fishman, Elliot, 2018. "Understanding the impacts of a public transit disruption on bicycle sharing mobility patterns: A case of Tube strike in London," Journal of Transport Geography, Elsevier, vol. 66(C), pages 154-166.
    18. Paul Peeters & Martin Landré, 2011. "The Emerging Global Tourism Geography—An Environmental Sustainability Perspective," Sustainability, MDPI, vol. 4(1), pages 1-30, December.
    19. Zhang, Xiaohu, 2021. "Beyond expected regularity of aggregate urban mobility: A case study of ridesourcing service," Journal of Transport Geography, Elsevier, vol. 95(C).
    20. He, Zhengbing, 2020. "Spatial-temporal fractal of urban agglomeration travel demand," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 549(C).

    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:eee:phsmap:v:580:y:2021:i:c:s0378437121004313. 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.