Weighted average geodesic distance of Vicsek network

Deng, Juan; Ye, Qianqian; Wang, Qin

doi:10.1016/j.physa.2019.121327

Cited by 43 publications

(4 citation statements)

References 19 publications

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“…In recent years, complex networks [1][2][3][4][5][6] have been widely researched because they are closely related to life and various disciplines. Real networks in life are abstracted into many interesting network models in unique iterative ways, such as Sierpinski gaskets [7][8][9], Vicsek fractals [10][11][12] and Koch curves [13,14]. The topological property [15,16] is the most basic and important content in the study of complex networks, which includes several features: average shortest path, clustering coefficient and degree distribution.…”

Section: Introductionmentioning

confidence: 99%

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

Li¹,

Li²,

Sun³

2021

J. Stat. Mech.

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In this paper, we focus on a network with even nodes named the weighted-crystal network, which is different from the regular iterative rules. By employing the self-similarity of the crystal network, we study and calculate the average receiving time (ART) and average weighted shortest path (AWSP) after dividing the network into n + 1 blocks. In particular, we pay attention to the hexagon crystal network in order to obtain exact results. The obtained scaled results show that ART grows linearly or sublinearly with the iterative and increases with the weight factor r. Meanwhile, the results of AWSP indicate that AWSP exhibits a sublinear dependence on the network order when r = 1. Otherwise, AWSP tends towards constants when 0 < r < 1.

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Section: Introductionmentioning

confidence: 99%

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

Li¹,

Li²,

Sun³

2021

J. Stat. Mech.

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“…Hence, it is natural to generalize the average geodesic distance from complex networks to self-similar fractals. Deng et al [24] obtained the average geodesic distances for Vicsek networks related to Vicsek fractal. Zhao et al [25] researched the average geodesic distance on the Sierpinski carpet in terms of the integral of geodesic distance on self-similar measure.…”

Section: Introductionmentioning

confidence: 99%

Structure properties and weighted average geodesic distances of the Sierpinski carpet fractal networks

et al. 2020

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In this paper, we consider the Sierpinski carpet fractal networks Gt constructed by the Sierpinski carpet F. Firstly, the structure properties of Gt, including degree distribution and clustering coefficient, are studied. Then, the weighted average geodesic distances of the Sierpinski carpet fractal F are analyzed by using the integral of geodesic distance in terms of self-similar measure with respect to the weight vector. Further the weighted average geodesic distances of the Sierpinski carpet fractal networks is obtained.

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“…In fact, there have been a great deal of treelike models proposed to model many complex networks. Hence a number of their topological structure properties have been reported, for instance, geodesic distance [9], mean first-passage time for random walk [10], fractal phenomena [11] and so on.…”

Section: Introductionmentioning

confidence: 99%

Exact solutions for geodesic distance on treelike models with some constraints

Luo¹,

Ma²,

Xu³

2019

Preprint

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Geodesic distance, commonly called shortest path length, has proved useful in a great variety of disciplines. It has been playing a significant role in search engine at present and so attracted considerable attention at the last few decades, particularly, almost all data structures and corresponding algorithms suitable to searching information generated based on treelike models. Hence, we, in this paper, study in detail geodesic distance on some treelike models which can be generated by three different types of operations, including first-order subdivision, (1, m)-star-fractal operation and m-vertex-operation. Compared to the most best used approaches for calculating geodesic distance on graphs, for instance, enumeration method and matrix multiplication, we take useful advantage of a novel method consisting in spirit of the concept of vertex cover in the language of graph theory and mapping. For each kind of treelike model addressed here, we certainly obtain an exact solution for its geodesic distance using our method. With the help of computer simulations, we confirm that the analytical results are in perfect agreement with simulations. In addition, we also report some intriguing structure properties on treelike models of two types among them. The one obeys exponential degree distribution seen in many complex networks, by contrast, the other possesses all but leaf vertices with identical degree and shows more homogeneous topological structure than the former. Besides that, the both have, in some sense, self-similar feature but instead the latter exhibits fractal property.

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Weighted average geodesic distance of Vicsek network

Cited by 43 publications

References 19 publications

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

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

Structure properties and weighted average geodesic distances of the Sierpinski carpet fractal networks

Exact solutions for geodesic distance on treelike models with some constraints

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