Evolving small-world networks with geographical attachment preference

Abstract. We present a family of scale-free network model consisting of cliques, which is established by a simple recursive algorithm. We investigate the networks both analytically and numerically. The obtained analytical solutions show that the networks follow a power-law degree distribution, with degree exponent continuously tuned between 2 and 3. The exact expression of clustering coefficient is also provided for the networks. Furthermore, the investigation of the average path length reveals that the networks possess small-world feature. Interestingly, we find that a special case of our model can be mapped into the Yule process. PACS

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“…By using the approach similar to that in [17,21,22,23], we can evaluate the APL of the present model.…”

Section: An Upper Bound Of Apl For General Casementioning

confidence: 99%

Evolving pseudofractal networks

2007

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“…Apollonian networks belong to a deterministic growing type of networks, which have drawn much attention from scientific communities [26,27,28,29,30,31,32,33,34,35]. The effects of the Apollonian networks on several dynamical models have been intensively studied, including Ising model and a magnetic * Electronic address: xinjizzz@sina.com (Z.Z.…”

Section: Introductionmentioning

confidence: 99%

Evolving Apollonian networks with small-world scale-free topologies

Zhang¹,

Rong²,

Zhou³

2006

Phys. Rev. E

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We propose two types of evolving networks: evolutionary Apollonian networks (EAN) and general deterministic Apollonian networks (GDAN), established by simple iteration algorithms. We investigate the two networks by both simulation and theoretical prediction. Analytical results show that both networks follow power-law degree distributions, with distribution exponents continuously tuned from 2 to 3. The accurate expression of clustering coefficient is also given for both networks. Moreover, the investigation of the average path length of EAN and the diameter of GDAN reveals that these two types of networks possess small-world feature. In addition, we study the collective synchronization behavior on some limitations of the EAN.

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“…Remark GF(t, 1) is exactly the graphs created by edge iterations [8], or evolving graphs with geographical attachment preference [9]. GFG can also be treated as a flower which has 3 × k same pedals, which are noting as P i (t), i = 1, 2, .…”

Section: Generation Of Farey-type Graphsmentioning

confidence: 99%

“…introduced Farey graphs (FG) which are simultaneously minimally 3-colorable, uniquely Hamiltonian, maximally outer-planar and perfect [6,7]. The merger of three FG coincides with the network created by edge iterations [8], or evolving graphs with geographical attachment preference [9]; while the combination of six FG generates the graphs with multidimensional growth [10]. Moreover, two new kinds of Farey-type graphs, the generalization of Farey graphs (GFG) and the extended Farey graphs (EFG), are deduced by generalizing the construction mechanism of FG, and they all are scale-free and small-world [11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Vertex Labeling and Routing for Farey-Type Symmetrically-Structured Graphs

Jiang¹,

Zhai²,

Zhuang³

et al. 2018

Preprint

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Abstract:The generalization of Farey graphs and extended Farey graphs are all originated from Farey graph and scale-free and small-world simultaneously. We propose a labeling of the vertices for it that allows determining all the shortest paths routing between any two vertices only based on their labels. The maximum number of shortest paths between any two vertices is huge as the product of two Fibonacci numbers, however, the label-based routing algorithm runs in linear time O(n). The existence of an efficient routing protocol for Farey-type models should help the understanding of several physical dynamic processes on it.

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Evolving small-world networks with geographical attachment preference

Cited by 43 publications

References 49 publications

Evolving pseudofractal networks

Evolving pseudofractal networks

Evolving Apollonian networks with small-world scale-free topologies

Vertex Labeling and Routing for Farey-Type Symmetrically-Structured Graphs

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