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

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  • 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
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    References listed on IDEAS

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    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.
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    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.
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