Eigentime Identities of Fractal Flower Networks

Ye, Qianqian; Gu, Jiangwen; Xi, Lifeng

doi:10.1142/s0218348x19500087

Cited by 14 publications

(3 citation statements)

References 22 publications

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“…Similarly, substitutions of nodes, rather then arcs, were considered in 15,16 . By constructing self-similar networks, Yao et al 16 proved that node substitution networks have the fractality property; see also [17][18][19] .…”

Section: Fig 1 a Substitution Networkmentioning

confidence: 99%

On the scale-freeness of random colored substitution networks

Li,

Britz

2021

Preprint

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Extending previous results in the literature, random colored substitution networks are introduced and are proved to be scale-free under natural conditions. Furthermore, the asymptotic node degrees, arc cardinalities and node cardinalities for these networks are derived. These results are achieved by proving stronger results regarding stochastic substitution processes, which form a new stochastic model that is here introduced.Many real-life phenomena are fractal in nature, including growth networks found in biology, brain connections and in social interactions. To study the properties of these networks, previous researchers introduced a mathematical model called substitution networks, to simulate the growth of the networks by iteratively replacing each arcs of a network by smaller networks. This model was later expanded by the introduction of arc colors to allow more types of arc replacements. However, these models are deterministic and do not allow for the randomness that real-life growth networks can exhibit. To capture this randomness, we expand the model to what we call random colored substitution networks, by allowing each arc to be replaced by a random choice of network. We describe properties of the randomly resulting networks, including their number of nodes and arcs and their node degrees. Our main result shows that these random colored substitution networks are scale-free and that they therefore have a particular type of structure.

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Section: Fig 1 a Substitution Networkmentioning

confidence: 99%

On the scale-freeness of random colored substitution networks

Li,

Britz

2021

Preprint

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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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“…We emphasize that it is difficult to obtain the above results if one utilizes the Newhouse thickness theorem [45]. The main reason is that it is not easy to calculate the thickness of K as there are very complicated overlaps in K. For the Assouad dimension of K and the geodesic distance on K × K, we refer to [36,38,51,50,37,56,47,49,48,46,53,35,52]. For the average weighted receiving time on the complex networks or on K, the readers can find results in the papers [23,6,7].…”

Section: Introductionmentioning

confidence: 99%

Multiple Representations of Real Numbers on Self-Similar Sets With Overlaps

et al. 2019

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Let K be the attractor of the following IFSThe main results of this paper are as follows:By virtue of Lemma 2.3, it follows thatLemma 2.12. If c ≥ (1 − λ) 2 , then K + K = [0, 2]. Proof. By Lemmas 2.1 and 2.11. Take I = J = [c − λ, c] ∪ [1 − λ, 1]. Therefore, for f (x, y) = x + y, we have f (I, J) = [2(c − λ), 2c] ∪ [c + 1 − 2λ, 1 + c] ∪ [2(1 − λ), 2]. By Lemma 2.3, we conculde that 2c − (c + 1 − 2λ) = c + 2λ − 1 ≥ 0, 1 + c − (2(1 − λ)) = c + 2λ − 1 ≥ 0.

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Eigentime Identities of Fractal Flower Networks

Cited by 14 publications

References 22 publications

On the scale-freeness of random colored substitution networks

On the scale-freeness of random colored substitution networks

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

Multiple Representations of Real Numbers on Self-Similar Sets With Overlaps

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