Average trapping time of weighted scale-free <i>m</i>-triangulation networks

Wu, Bo; Chen, Yingying; Zhang, Zhizhuo; Su, Weiyi

doi:10.1088/1742-5468/ab38c0

Cited by 11 publications

(7 citation statements)

References 22 publications

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“…Figure 9 shows the numerical values of T global (n) as a function of N for different w and m = 2, m = 5. The results confirm the asymptotic behavior in equation (41).…”

Section: J Stat Mech (2021) 063405supporting

confidence: 82%

“…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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“…Figure 9 shows the numerical values of T global (n) as a function of N for different w and m = 2, m = 5. The results confirm the asymptotic behavior in equation (41).…”

Section: J Stat Mech (2021) 063405supporting

confidence: 82%

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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show abstract

“…Thirdly, introducing more traps can lower AT T and improve trapping efficiency. To some extent, conclusions made here and in previous works such as [30], [40], [41], [46]- [48] may collectively serve as pieces of puzzles for illuminating trapping issue and related dynamical processes on more general networks or systems.…”

Section: B Explicit Expressions Of Average Trapping Timementioning

confidence: 52%

Exploring Trapping Problem on Weighted Heterogeneous Networks Induced by Extended Corona Product

2020

IEEE Access

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Since many dynamical processes can be analyzed in the framework of trapping problem, it is great important to explore trapping problem on diverse complex systems or networks. However, addressing trapping problem on networks generated by graph products is still less touched. In this paper, by taking type of random walks and number of traps into account and compiling four different scenarios, trapping problem is touched more completely on resultant weighted heterogeneous networks of extended corona product and weight reinforcement mechanism. In more detail, we study standard random walk and delayed random walk on the network with a deep trap fixed at one initial node in the first and second scenarios respectively. This two types of random walks are further investigated on the network with three traps placed at initial three nodes in more challenging third and fourth scenarios. In all this four scenarios, the solutions of average trapping time(AT T) are deduced analytically to measure trapping efficiency, which agree well with their corresponding numerical counterparts and show that AT T grows sub-linearly with network size. Besides, expressions of AT T obtained in the second and fourth scenarios indicate that the parameter p governing delayed random walk alters the pre-factor of AT T but has no effect on the leading scaling of AT T. Furthermore, the comparisons between expression of AT T in first and third scenarios, expression of AT T in second and fourth scenarios imply that AT T can be lowered and trapping efficiency can be improved accordingly by introducing more traps. In summary, this work may enrich the clues for understanding trapping issue and modulating trapping process on more general heterogeneous weighted networks.

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

Cited by 11 publications

References 22 publications

Trapping efficiency of random walks on weighted scale-free trees

Trapping efficiency of random walks on weighted scale-free trees

Exploring Trapping Problem on Weighted Heterogeneous Networks Induced by Extended Corona Product

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

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