The trapping problem and the average shortest weighted path of the weighted pseudofractal scale-free networks

Meifeng Dai (), Changxi Dai (), Huiling Wu, Xianbin Wu (), Wenjing Feng () and Weiyi Su ()
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Meifeng Dai: Institute of Applied System Analysis, Jiangsu University, Zhenjiang 212013, P. R. China
Changxi Dai: Institute of Applied System Analysis, Jiangsu University, Zhenjiang 212013, P. R. China
Huiling Wu: #x2020;Junior College, Zhejiang Wanli University, Ningbo, Zhejiang 315100, P. R. China
Xianbin Wu: #x2020;Junior College, Zhejiang Wanli University, Ningbo, Zhejiang 315100, P. R. China
Wenjing Feng: Institute of Applied System Analysis, Jiangsu University, Zhenjiang 212013, P. R. China
Weiyi Su: #x2021;Department of Mathematics, Nanjing University, Nanjing 210093, P. R. China

International Journal of Modern Physics C (IJMPC), 2019, vol. 30, issue 01, 1-17

Abstract: In this paper, we study the trapping time in the weighted pseudofractal scale-free networks (WPSFNs) and the average shortest weighted path in the modified weighted pseudofractal scale-free networks (MWPSFNs) with the weight factor r. At first, for exceptional case with the trap fixed at a hub node for weight-dependent walk, we derive the exact analytic formulas of the trapping time through the structure of WPSFNs. The obtained rigorous solution shows that the trapping time approximately grows as a power-law function of the number of network nodes with the exponent represented by ln2+4r2+rln3. Then, we deduce the scaling expression of the average shortest weighted path through the iterative process of the construction of MWPSFNs. The obtained rigorous solution shows that the scalings of average shortest weighted path with network size obey three laws along with the range of the weight factor. We provide a theoretical study of the trapping time for weight-dependent walk and the average shortest weighted path in a wide range of deterministic weighted networks.

Keywords: Trapping time; average shortest weighted path; weighted pseudofractal scale-free networks; weight-dependent walk (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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DOI: 10.1142/S0129183119500104

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