IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v523y2019icp268-278.html
   My bibliography  Save this article

Mean first-passage times for two biased walks on the weighted rose networks

Author

Listed:
  • Dai, Meifeng
  • Dai, Changxi
  • Ju, Tingting
  • Shen, Junjie
  • Sun, Yu
  • Su, Weiyi

Abstract

Compared with traditional random walk, biased walks have been studied extensively over the past decade especially in the transport and communication networks. In this paper, we first introduce the weighted rose networks. Then, for the weighted rose networks we focus on two biased walks, maximal entropy walk and weight-dependent walk, and obtain the exact expressions of their stationary distributions and mean first-passage times. Finally, we find that the average receiving time for maximal entropy walk is a quadratic function of the weight parameter r while the average receiving time for weighted-dependent walk is a linear function of the weight parameter r. Meanwhile, for the maximal entropy walk, the smaller the value of r is, the more efficient the trapping process is. For the weighted-dependent walk, the larger the value of r(rr0≈2.6) is, the more efficient for the weight-dependent walk.

Suggested Citation

  • Dai, Meifeng & Dai, Changxi & Ju, Tingting & Shen, Junjie & Sun, Yu & Su, Weiyi, 2019. "Mean first-passage times for two biased walks on the weighted rose networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 268-278.
  • Handle: RePEc:eee:phsmap:v:523:y:2019:i:c:p:268-278
    DOI: 10.1016/j.physa.2019.01.112
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437119301190
    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.2019.01.112?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. Meifeng Dai & Yufei Chen & Xiaoqian Wang & Weiyi Su, 2018. "Spectral analysis for weighted iterated quadrilateral graphs," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 29(11), pages 1-20, November.
    2. 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.
    3. Ye, Dandan & Dai, Meifeng & Sun, Yanqiu & Shao, Shuxiang & Xie, Qi, 2016. "Average receiving scaling of the weighted polygon Koch networks with the weight-dependent walk," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 458(C), pages 1-8.
    4. Dai, Meifeng & Chen, Dandan & Dong, Yujuan & Liu, Jie, 2012. "Scaling of average receiving time and average weighted shortest path on weighted Koch networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(23), pages 6165-6173.
    5. Yang, Jinjin & Wang, Songjing & Xi, Lifeng & Ye, Yongchao, 2018. "Average geodesic distance of skeleton networks of Sierpinski tetrahedron," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 495(C), pages 269-277.
    6. Xiaoqian Wang & Meifeng Dai & Yufei Chen & Yue Zong & Yu Sun & Weiyi Su, 2018. "Determining entire mean first-passage time for Cayley networks," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 29(01), pages 1-10, January.
    7. 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.
    8. 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.
    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. Hu, Zhongren & Wu, Bo, 2023. "The average shortest distance of three colored substitution networks," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    2. Wu, Bo & Zhang, Zhizhuo, 2020. "The average trapping time on a half Sierpinski Gasket," Chaos, Solitons & Fractals, Elsevier, vol. 140(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. 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.
    2. 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.
    3. Liu, Jia-Bao & Zhao, Jing & Cai, Zheng-Qun, 2020. "On the generalized adjacency, Laplacian and signless Laplacian spectra of the weighted edge corona networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    4. 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.
    5. Hu, Zhongren & Wu, Bo, 2023. "The average shortest distance of three colored substitution networks," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    6. Dai, Meifeng & Feng, Wenjing & Wu, Xianbin & Chi, Huijia & Li, Peng & Su, Weiyi, 2019. "The Laplacian spectrum and average trapping time for weighted Dyson hierarchical network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 510-518.
    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. Lu, Ying & Xu, Jiajun & Xi, Lifeng, 2023. "Fractal version of hyper-Wiener index," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    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.
    10. Dai, Meifeng & Shao, Shuxiang & Su, Weiyi & Xi, Lifeng & Sun, Yanqiu, 2017. "The modified box dimension and average weighted receiving time of the weighted hierarchical graph," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 475(C), pages 46-58.
    11. Zeng, Cheng & Xue, Yumei & Huang, Yuke, 2021. "Fractal networks with Sturmian structure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 574(C).
    12. 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.
    13. Sun, Jun-yan & Tang, Jian-ming & Fu, Wei-ping & Wu, Bing-ying, 2017. "Hybrid modeling and empirical analysis of automobile supply chain network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 377-389.
    14. Ma, Fei & Wang, Ping & Yao, Bing, 2021. "Random walks on Fibonacci treelike models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 581(C).
    15. 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.
    16. Jiao, Bo & Nie, Yuan-ping & Shi, Jian-mai & Huang, Cheng-dong & Zhou, Ying & Du, Jing & Guo, Rong-hua & Tao, Ye-rong, 2016. "Scaling of weighted spectral distribution in deterministic scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 451(C), pages 632-645.
    17. Sun, Yu & Dai, Meifeng & Xi, Lifeng, 2014. "Scaling of average weighted shortest path and average receiving time on weighted hierarchical networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 407(C), pages 110-118.
    18. 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.
    19. Huang, Liang & Zheng, Yu, 2023. "Asymptotic formula on APL of fractal evolving networks generated by Durer Pentagon," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    20. 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).

    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:523:y:2019:i:c:p:268-278. 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.