The average trapping time on the weighted pseudofractal scale-free web

Wu, Bo

doi:10.1088/1742-5468/ab7af0

Cited by 10 publications

(4 citation statements)

References 34 publications

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“…There have also been important efforts devoted to improving the trapping efficiency by designing a suitable biased random walk strategy [37][38][39]. On weighted networks, the values of the ATT can be reduced by setting weights of the network and design a biased random walk strategy properly [40][41][42][43][44]. However, these works just focus on the ATT for some particular sites.…”

Section: Introductionmentioning

confidence: 99%

Trapping efficiency of random walks on weighted scale-free trees

Gao¹,

Peng²,

Tang³

et al. 2021

J. Stat. Mech.

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Trapping processes of random walks on networks have a wide range of applications and have become a research hot spot in the past few decades. Two important measures characterizing the trapping efficiency on networks are the average trapping time (ATT) and the global mean first-passage times (GMFPT). ATT is the expected time for a random walker starting from a random site to reach a fixed target site for the first time, and GMFPT is obtained from the average of ATTs over all possible target sites. In this paper, we study biased random walks on two types of weighted scale-free trees with non-fractal and fractal structures, whose weights are characterized by a real parameter w (w > 0). In the first part, we analytically evaluate the ATT on non-fractal weighted trees with a trap fixed in a hub node (node with the highest degree). Next, we present a method to calculate the GMFPT for biased random walks on general weighted networks, and analytically evaluate this quantity for fractal and non-fractal weighted scale-free trees. Finally, we analyze the effect of the parameter w on the trapping efficiency. The results for the trapping efficiency measured by the ATT for a trap fixed at a hub node show that in the non-fractal case the ATT increases monotonically as w decreases; for the trapping efficiency measured by the GMFPT, it is possible to obtain higher trapping efficiency on fractal trees by setting w properly. In contrast, for the non-fractal case, the highest trapping efficiency is produced in unweighted networks (w = 1), whereas for other values of w, the GMFPT is higher, revealing a reduction in the trapping frequency.

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Section: Introductionmentioning

confidence: 99%

Trapping efficiency of random walks on weighted scale-free trees

Gao¹,

Peng²,

Tang³

et al. 2021

J. Stat. Mech.

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“…For the content of probability generating function, you can refer to reference [33]. For the convenience of subsequent use, this paper briefly lists relevant knowledge.…”

Section: Probability Generating Functionmentioning

confidence: 99%

The average trapping time of non-nearest-neighbor jumps on nested networks

Han,

2023

Phys. Scr.

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In this paper, we consider the trapping problem on the nearest-neighbor (NN) and non-nearest-neighbor (NNN) jumps on nested networks. Based on the nested construction of the network and the use of probability generating function tool, the iterative rules of two successive generations of the network are found, and the analytical expression of the average trapping time (ATT) is finally obtained. We allow two jump modes in the network at the same time, and the results show that the choice probability of the jump mode is not related to the exponential term of the scaling expression, but to its leading factor term. According to the analytic solution of ATT, we can find that the value of ATT expands superlinearly with the increase of network size. In addition, the numerical simulation results of parameters q (the probability of choosing NNN jump) and n (the generation of the network) show that with fixed n, ATT decreases with the increase of q; while with fixed q, ATT increases with the increase of n. In summary, this work can observe the effect of different hopping modes on random walk efficiency in complex networks.

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“…[11,12] presented different expansions of the weighted Koch network; Refs. [13,14] studied ATT on the pseudofractal network by different ways. Besides, Wu et al [15] considered a particular weighted hierarchical graph H(n, k) where n represents the iterative times and k represents the number of nodes of the complete graph, so the simplest iterated graph was got when k = 3.…”

Section: Introductionmentioning

confidence: 99%

Average trapping time on the weighted hierarchical triangle network with primary node iteration

Li¹,

Lu²

2023

ScienceAsia

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In this paper, we consider the average trapping time (ATT) on the weighted hierarchical triangle network with primary node iteration. Firstly, the structure with primary node iteration is shown, then ATT is studied and the exact expression is obtained based on the self-similarity of the network. The results illustrate that ATT grows linearly or sublinearly with the iterative times at different weights and with increasing weights. Besides, compared to the network without primary node iteration, the network with primary node iteration is more efficient in random walks and the difference is greater with increasing weights. When the weight is small, there is little difference.

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The average trapping time on the weighted pseudofractal scale-free web

Cited by 10 publications

References 34 publications

Trapping efficiency of random walks on weighted scale-free trees

Trapping efficiency of random walks on weighted scale-free trees

The average trapping time of non-nearest-neighbor jumps on nested networks

Average trapping time on the weighted hierarchical triangle network with primary node iteration

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