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Scaling law of diffusion processes on fractal networks

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  • Feng, Shiyuan
  • Weng, Tongfeng
  • Chen, Xiaolu
  • Ren, Zhuoming
  • Su, Chang
  • Li, Chunzi

Abstract

We investigate diffusion processes on fractal networks at different length scales. This is achieved by the application of a box covering procedure. We find that a clearly scaling law emerges on a great variety of fractal networks. Specifically, a number of metrics for quantifying diffusion processes, such as Kemeny’s constant, the expected search time and its variation, follow a power-law with the number of boxes for covering. Furthermore, we identify a power-law relation between energy and the number of boxes. Remarkably, we show that the expected time for hunting a moving target similarly presents a power law behavior on a given fractal network. Our work reveals that scaling law is a common characteristic of fractal networks beyond their structural organization.

Suggested Citation

  • Feng, Shiyuan & Weng, Tongfeng & Chen, Xiaolu & Ren, Zhuoming & Su, Chang & Li, Chunzi, 2024. "Scaling law of diffusion processes on fractal networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 640(C).
    • Handle: RePEc:eee:phsmap:v:640:y:2024:i:c:s0378437124002139
    DOI: 10.1016/j.physa.2024.129704
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    References listed on IDEAS

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