Scaling law of diffusion processes on fractal networks

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

Physica A: Statistical Mechanics and its Applications, 2024, vol. 640, issue C

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.

Keywords: Scaling law; Diffusion processes; Fractal networks; Structural organization (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:640:y:2024:i:c:s0378437124002139

DOI: 10.1016/j.physa.2024.129704

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