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

Dai, Meifeng; Zong, Yue; He, Jiaojiao; Wang, Xiaoqian; Sun, Yu; Su, Weiyi

doi:10.1038/s41598-018-19959-x

Cited by 21 publications

(5 citation statements)

References 24 publications

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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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Section: Introductionmentioning

confidence: 99%

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

Chen

Zhang

et al. 2019

J. Stat. Mech.

Self Cite

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“…As to the trapping problem, many existing research literatures have explored the trapping time problem on different networks, such as scale-free trees [18][19][20], weighted directed networks [21], (u, v) flower networks [22][23][24], etc [25,26]. For a class of classical self-similar network called Sierpinski gasket (SG), scholars have studied many properties on it, such as the average trapping time (ATT), the mean first passage time (MFPT), the first return time (FRT), and so on.…”

Section: Introductionmentioning

confidence: 99%

The trapping problem on horizontal partitioned level-3 sierpinski gasket networks

Chen

2023

Phys. Scr.

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Random walk on complex networks is a research hotspot nowadays. The average trapping time (ATT) is an important property related to the trapping problem, which is a variant of random walk, because it can be used to measure the transmission efficiency of particles randomly walking on the network. In this paper, we consider the trapping problem on the horizontal partitioned level-3 Sierpinski gasket network which is determined by the cutting line lk, that is, by the partition coefficient k. Then through the structure of this research model, we derive the exact analytical expression of the ATT. Furthermore, we draw two kinds of numerical simulation diagrams to simulate the relationship between the ATT and the iteration number and the partition coefficient, and compare them with the ATT on the original graph (uncut). The obtained solution shows that the ATT is affected by the k, specifically, the larger the k, the shorter the ATT, that is the higher the transmission efficiency.

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“…Most of the previous research on random walks about complex networks focuses on two aspects: one is that the nodes of the studied network have identical walking rules [ 13 , 14 ], and the other is to study random walks on heterogeneous networks that set a trap on the node with the largest degree and have scale-free characteristics [ 15 , 16 , 17 ]. Since many real networks have a scale-free nature, every node in the network can be a trap.…”

Section: Introductionmentioning

confidence: 99%

Mean Hitting Time for Random Walks on a Class of Sparse Networks

Wang

Yao

2021

Entropy

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For random walks on a complex network, the configuration of a network that provides optimal or suboptimal navigation efficiency is meaningful research. It has been proven that a complete graph has the exact minimal mean hitting time, which grows linearly with the network order. In this paper, we present a class of sparse networks G(t) in view of a graphic operation, which have a similar dynamic process with the complete graph; however, their topological properties are different. We capture that G(t) has a remarkable scale-free nature that exists in most real networks and give the recursive relations of several related matrices for the studied network. According to the connections between random walks and electrical networks, three types of graph invariants are calculated, including regular Kirchhoff index, M-Kirchhoff index and A-Kirchhoff index. We derive the closed-form solutions for the mean hitting time of G(t), and our results show that the dominant scaling of which exhibits the same behavior as that of a complete graph. The result could be considered when designing networks with high navigation efficiency.

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

Cited by 21 publications

References 24 publications

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

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

The trapping problem on horizontal partitioned level-3 sierpinski gasket networks

Mean Hitting Time for Random Walks on a Class of Sparse Networks

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