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Random walks and diameter of finite scale-free networks

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  • Lee, Sungmin
  • Yook, Soon-Hyung
  • Kim, Yup

Abstract

Dynamical scalings for the end-to-end distance Ree and the number of distinct visited nodes Nv of random walks (RWs) on finite scale-free networks (SFNs) are studied numerically. 〈Ree〉 shows the dynamical scaling behavior 〈Ree(ℓ¯,t)〉=ℓ¯α(γ,N)g(t/ℓ¯z), where ℓ¯ is the average minimum distance between all possible pairs of nodes in the network, N is the number of nodes, γ is the degree exponent of the SFN and t is the step number of RWs. Especially, 〈Ree(ℓ¯,t)〉 in the limit t→∞ satisfies the relation 〈Ree〉∼ℓ¯α∼dα, where d is the diameter of network with d(ℓ¯)≃lnN for γ≥3 or d(ℓ¯)≃lnlnN for γ<3. Based on the scaling relation 〈Ree〉, we also find that the scaling behavior of the diameter of networks can be measured very efficiently by using RWs.

Suggested Citation

  • Lee, Sungmin & Yook, Soon-Hyung & Kim, Yup, 2008. "Random walks and diameter of finite scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(12), pages 3033-3038.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:12:p:3033-3038
    DOI: 10.1016/j.physa.2008.01.101
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    Cited by:

    1. Huang, Wei & Chen, Shengyong & Wang, Wanliang, 2014. "Navigation in spatial networks: A survey," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 393(C), pages 132-154.

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    Keywords

    Complex networks; Random walks;

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