Eigentime identities of flower networks with multiple branches

Xi, Lifeng; Ye, Qianqian; Yao, Jialing; Sun, Bingbin

doi:10.1016/j.physa.2019.04.093

Cited by 3 publications

(1 citation statement)

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“…where the sum is taken over all the nonzero eigenvalues of the normalized Laplacian matrix of Γ. For recent work on eigentime identities of flower networks with multiple branches and weighted scale-free triangulation networks, we refer the reader to [34,35]. We shall give an explicit formula of ( 6) for hype-cubes.…”

Section: Applications Of Normalized Laplacian Spectrummentioning

confidence: 99%

The normalized Laplacian spectrum and eigentime identities of hype-cubes

Chen,

Zhao

2019

Preprint

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Many popular graph metrics encode average properties of individual network elements. Complementing these conventional graph metrics, the eigenvalue spectrum of the normalized Laplacian describes a network's structure directly at a systems level, without referring to individual nodes or connections. In this paper, we study the spectrum and their applications of normalized Laplacian matrices of hype-cubes, a special kind of Cayley graphs. We determine explicitly all the eigenvalues and their corresponding multiplicities by a recursive method. By using the relation between normalized Laplacian spectrum and eigentime identity, we derive the explicit formula to the eigentime identity for random walks on the hype-cubes and show that it grows linearly with the network size. Moreover, we compute the number of spanning trees of the hype-cubes.

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Section: Applications Of Normalized Laplacian Spectrummentioning

confidence: 99%

The normalized Laplacian spectrum and eigentime identities of hype-cubes

Chen,

Zhao

2019

Preprint

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Spectra of generalized windmill networks: Analytical solutions and applications

Liao

Aziz-Alaoui

Chen

2020

Int. J. Mod. Phys. C

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The generalized windmill graphs are good models for many real-world networks. In this paper, we obtain analytic expressions for the eigenvalues of the adjacency matrices and of the Laplacian matrices of the generalized windmill graphs. Using this information, we study some structural and dynamical properties of these graphs. To the end, we investigate the metro networks of four France cities and propose our suggestions for the planning of public transport networks.

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Fractal Version of Zagreb Eccentricity Index

Lü

2023

Fractals

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Eigentime identities of flower networks with multiple branches

Cited by 3 publications

References 35 publications

The normalized Laplacian spectrum and eigentime identities of hype-cubes

The normalized Laplacian spectrum and eigentime identities of hype-cubes

Spectra of generalized windmill networks: Analytical solutions and applications

Fractal Version of Zagreb Eccentricity Index

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