Mixed random walks with a trap in scale-free networks including nearest-neighbor and next-nearest-neighbor jumps

Zhang, Zhongzhi; Dong, Yuze; Sheng, Yibin

doi:10.1063/1.4931988

Cited by 15 publications

(6 citation statements)

References 61 publications

(78 reference statements)

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“…That is to say, the smaller the ATT, the higher the diusion eciency of the network. Previous studies have focused on trapping time problem in binary networks [8][9][10], but seldom on weighted networks. However, weighted networks have more practical applications.…”

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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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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“…Intuited by scale-free binary networks 21 and weighted tree networks 22 , the weighted scale-free treelike networks, denoted by F n ( n ≥ 0), are built iteratively.…”

Section: Resultsmentioning

confidence: 99%

“…The walker jumps to one of nearest neighbor nodes (next-nearest neighbor nodes) with the standard weight-dependent walks. If the current location of the walker is a new node created at generation n , then the walker can only jump to one of the nearest neighbor nodes with the standard weight-dependent walks 21 . …”

Section: Resultsmentioning

confidence: 99%

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Two types of weight-dependent walks with a trap in weighted scale-free treelike networks

Dai

Zong

et al. 2018

Sci Rep

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In this paper, we present the weighted scale-free treelike networks controlled by the weight factor r and the parameter m. Based on the network structure, we study two types of weight-dependent walks with a highest-degree trap. One is standard weight-dependent walk, while the other is mixed weight-dependent walk including both nearest-neighbor and next-nearest-neighbor jumps. Although some properties have been revealed in weighted networks, studies on mixed weight-dependent walks are still less and remain a challenge. For the weighted scale-free treelike network, we derive exact solutions of the average trapping time (ATT) measuring the efficiency of the trapping process. The obtained results show that ATT is related to weight factor r, parameter m and spectral dimension of the weighted network. We find that in different range of the weight factor r, the leading term of ATT grows differently, i.e., superlinearly, linearly and sublinearly with the network size. Furthermore, the obtained results show that changing the walking rule has no effect on the leading scaling of the trapping efficiency. All results in this paper can help us get deeper understanding about the effect of link weight, network structure and the walking rule on the properties and functions of complex networks.

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“…The quantities we are interested in are the first passage time (FPT), which is the time it takes a random walker to reach a given site for the first time, and first return time (FRT), which is the time it takes a random walker to return to the starting site for the first time [25][26][27][28][29][30][31][32] . In the past several years, a lot of work was devoted to analyze the mean 12,[33][34][35][36][37][38][39][40][41][42] and the variance 25,[43][44][45][46] of the two random variables on different networks. The mean provides valuable estimate of the random variable and the variance is good measure on whether the estimate provided by the mean is reliable.…”

Section: Introductionmentioning

confidence: 99%

Scaling properties of first-passage quantities on the fractal and transfractal scale free networks

Peng

2016

Preprint

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Fractal (or transfractal) and scale free characters are common properties of real life network systems. It is of great significance to uncover the effect of these characters on the dynamic processes taking place on complex medias. In this paper, we consider the random walk process on a kind of fractal (or transfractal) scale free networks, which also called as (u, v) flowers, and we focus on the global first passage time (GFPT) and first return time (FRT). Here, we present method to derive exactly the probability generation function, mean and variance of the GFPT and FRT for a given hub (i.e., node with the highest degree) and then the scaling properties of the mean and the variance of the GFPT and FRT are disclosed. Our results show that, for the case of u > 1, while the networks are fractals, the mean of the GFPT scales with the volume of the network as, where * denotes the mean of random variable * , N t is the volume of the network with generation t and d s is the spectral dimension of the network; but, for the case of u = 1, while the networks are nonfractals, the mean of the GFPT scales as GM F P T t ∼ N 2/ ds t , where ds is the transspectral dimension of the network, which is introduced in this paper. Results also show that, the variance of the GFPT scales as V ar(GF P T t ) ∼ GF P T t 2 , where V ar( * ) denotes variance of of random variable * ; whereas the variance of the FRT scales as V ar(F RT t ) ∼ F RT t GF P T t . Our results imply that for the case that the networks are nonfractals, the mean and the variance of the GFPT are not controlled by the spectral dimension(i.e., d s = 2), but they are controlled by the transspectral dimension. In order to evaluate the fluctuation of the GFPT and FRT, we also calculate the reduced moments of the the GFPT and FRT and find that, in the limit of large size, the reduced moment of the FRT tends to be infinite, whereas the reduced moment of the GFPT is almost a const.Therefore, on the (u, v) flowers of large size, the fluctuation of the FRT is huge, whereas the fluctuation of the GFPT is much smaller.

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Mixed random walks with a trap in scale-free networks including nearest-neighbor and next-nearest-neighbor jumps

Cited by 15 publications

References 61 publications

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

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

Two types of weight-dependent walks with a trap in weighted scale-free treelike networks

Scaling properties of first-passage quantities on the fractal and transfractal scale free networks

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