Fractality of multiple colored substitution networks

Li, Ziyu; Yao, Jialing; Wang, Qin

doi:10.1016/j.physa.2019.03.079

Cited by 8 publications

(1 citation statement)

References 21 publications

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“…Xi et al proved that substitution networks have the scale-free property, as well as the related fractality property. Li et al 13,14 proved that substitution networks retain the scale-free property in the more general setting of colored arcs and fixed networks to replace each arc of a given color. They also showed that certain of these colored substitution networks have the fractality property.…”

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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The average shortest distance of three colored substitution networks

Hu,

2023

Chaos, Solitons & Fractals

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On the scale-freeness of random colored substitution networks

Li¹,

Britz

2024

Proc. Amer. Math. Soc.

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Extending previous results in the literature, random colored substitution networks and degree dimension are defined in this paper. The scale-freeness of these networks is proved by introducing a new definition for degree dimension that is associated with Lyapunov exponents. The random colored substitution network hence turns out to be a simple, powerful and promising model to generate random scale-free networks.

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Fractality of multiple colored substitution networks

Cited by 8 publications

References 21 publications

On the scale-freeness of random colored substitution networks

On the scale-freeness of random colored substitution networks

The average shortest distance of three colored substitution networks

On the scale-freeness of random colored substitution networks

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