The trapping problem of the weighted scale-free treelike networks for two kinds of biased walks

Dai, Meifeng; Zong, Yue; He, Jiaojiao; Sun, Yu; Shen, Chunyu; Su, Weiyi

doi:10.1063/1.5045829

Cited by 16 publications

(7 citation statements)

References 51 publications

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“…In this section, we explore the trapping efficiency on WNFSFTs, where analytical results for WFSFT are derived in [44]. Let us consider the trapping problem for a trap placed at a hub node (e.g.…”

Section: Trapping With a Trap Fixed At A Hub Node On Wnfsftmentioning

confidence: 99%

“…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%

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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: Trapping With a Trap Fixed At A Hub Node On Wnfsftmentioning

confidence: 99%

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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“…Therefore, it is very natural and important to study diusion on weighted scale-free networks. In recent years, Dai et al have studied the dynamic processes on scaleless networks with dierent networks, including weighted pseudofractal scal-free networks, weighted scale-free triangulation networks and so on [13][14][15][16][17][18][19]. Based on the J. Stat.…”

Section: Introductionmentioning

confidence: 99%

Average trapping time of weighted scale-free m-triangulation networks

Chen

Zhang

et al. 2019

J. Stat. Mech.

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This paper investigates the average trapping time (ATT) on weighted scale-free m-triangulation networks. ATT is the mean of the firstpassage time from any node to the trap fixed at a hub node over the entire network. Based on the structural properties of weighted scale-free m-triangulation networks, we deduce the accurate expression of ATT for weight-dependent walk. The result shows that the scaling expression of ATT with network size obeys a power-law function with exponent ln 2+4mr 2+mr ln(2m+1) characterized by the weight factor r and the growth factor m. Further, we find that the parameters r and m have a significant impact on the diusion eciency of the network, namely, the smaller r and m are, the more ecient the trapping process of the network is.

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“…There are also many works devoted to improving the transport efficiency by designing appropriate biased random walk strategies [28][29][30]. By introducing the proper weight to each edge of the network and designing a proper biased random walk strategy, one can shorten the MFPT to obtain higher transport efficiency on the underling networks [31][32][33][34][35]. One can also shorten the GMFPT for random walks on some networks [36].…”

Section: Introductionmentioning

confidence: 99%

Optimizing the First-Passage Process on a Class of Fractal Scale-Free Trees

2021

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First-passage processes on fractals are of particular importance since fractals are ubiquitous in nature, and first-passage processes are fundamental dynamic processes that have wide applications. The global mean first-passage time (GMFPT), which is the expected time for a walker (or a particle) to first reach the given target site while the probability distribution for the position of target site is uniform, is a useful indicator for the transport efficiency of the whole network. The smaller the GMFPT, the faster the mass is transported on the network. In this work, we consider the first-passage process on a class of fractal scale-free trees (FSTs), aiming at speeding up the first-passage process on the FSTs. Firstly, we analyze the global mean first-passage time (GMFPT) for unbiased random walks on the FSTs. Then we introduce proper weight, dominated by a parameter w(w>0), to each edge of the FSTs and construct a biased random walks strategy based on these weights. Next, we analytically evaluated the GMFPT for biased random walks on the FSTs. The exact results of the GMFPT for unbiased and biased random walks on the FSTs are both obtained. Finally, we view the GMFPT as a function of parameter w and find the point where the GMFPT achieves its minimum. The exact result is obtained and a way to optimize and speed up the first-passage process on the FSTs is presented.

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The trapping problem of the weighted scale-free treelike networks for two kinds of biased walks

Cited by 16 publications

References 51 publications

Trapping efficiency of random walks on weighted scale-free trees

Trapping efficiency of random walks on weighted scale-free trees

Average trapping time of weighted scale-free m-triangulation networks

Optimizing the First-Passage Process on a Class of Fractal Scale-Free Trees

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