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Eigentime identities for random walks on a family of treelike networks and polymer networks

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  • Dai, Meifeng
  • Wang, Xiaoqian
  • Sun, Yanqiu
  • Sun, Yu
  • Su, Weiyi

Abstract

In this paper, we investigate the eigentime identities quantifying as the sum of reciprocals of all nonzero normalized Laplacian eigenvalues on a family of treelike networks and the polymer networks. Firstly, for a family of treelike networks, it is shown that all their eigenvalues can be obtained by computing the roots of several small-degree polynomials defined recursively. We obtain the scalings of the eigentime identity on a family of treelike with network size Nn is NnlnNn. Then, for the polymer networks, we apply the spectral decimation approach to determine analytically all the eigenvalues and their corresponding multiplicities. Using the relationship between the generation and the next generation of eigenvalues we obtain the scalings of the eigentime identity on the polymer networks with network size Nn is NnlnNn. By comparing the eigentime identities on these two kinds of networks, their scalings with network size Nn are all NnlnNn.

Suggested Citation

  • Dai, Meifeng & Wang, Xiaoqian & Sun, Yanqiu & Sun, Yu & Su, Weiyi, 2017. "Eigentime identities for random walks on a family of treelike networks and polymer networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 484(C), pages 132-140.
    • Handle: RePEc:eee:phsmap:v:484:y:2017:i:c:p:132-140
    DOI: 10.1016/j.physa.2017.04.172
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Carletti, Timoteo & Righi, Simone, 2010. "Weighted Fractal Networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(10), pages 2134-2142.
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    Cited by:

    1. 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.

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