Scaling of average receiving time and average weighted shortest path on weighted-crystal network

Li, Jun; Li, Xiaoyan; Sun, Yu

doi:10.1088/1742-5468/ac1409

Cited by 3 publications

(2 citation statements)

References 32 publications

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“…The diffusion efficiency is inversely proportional to the value of ATT, that is, the smaller the ATT, the higher the diffusion efficiency of the network; the larger the ATT, the lower the diffusion efficiency of the network. Relevant scholars have studied the trapping problem in triangle network [17], crystal network [22], flower network [23,24], ring tree network [25,26], fractal network [27], SG network [28], etc., and obtained the analytical formula of ATT. The walking style of these problems considers a simple random walk, that is, moving from a node to its nearest neighbor (NN) node.…”

Section: Introductionmentioning

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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Section: Introductionmentioning

confidence: 99%

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

Han,

2023

Phys. Scr.

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“…But different nodes may occupy different status in practice, which is why Ref. [16] introduced primary nodes and secondary nodes. The constructed network iterates only over the primary nodes, so primary nodes occupy a dominant position and have stronger iterated capability.…”

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 effect of weight heterogeneity on the shortest path of weighted Cayley network

Han,

2024

Int. J. Mod. Phys. C

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In this paper, we introduce the weighted Cayley network parameterized by three weight parameters r,q,g. The average weighted shortest path (AWSP) is calculated and its expression is derived. The results show that the AWSP of the network forms 10 laws with the range of weights r, q and g, and two laws based on single weight factor are generalized. From these 10 laws, we can see more clearly: When the average value of the weight factors ([Formula: see text]) of the three branches is fixed, the larger the variance is, the larger the value of AWSP is; When the weight factor of any of the three branches is equal to [Formula: see text], its AWSP value growth law is the same as that of the weight factor of 0 to 1, there is no special change; When any weight factor of the three branches is equal to 1, the network mainly grows with the logarithm of the network size. Meanwhile, the growth of the network has no boundary, but AWSP maintains a bounded state, and the growth rate of AWSP will be faster when the number of branch weights equal to 1 is more.

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Scaling of average receiving time and average weighted shortest path on weighted-crystal network

Cited by 3 publications

References 32 publications

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

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

The effect of weight heterogeneity on the shortest path of weighted Cayley network

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