The normalized Laplacian spectrum and eigentime identities of hype-cubes

Yangyang Chen; Yi Zhao

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arXiv · 1909.06782

The normalized Laplacian spectrum and eigentime identities of hype-cubes

Yangyang Chen·Yi Zhao

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Abstract

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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BibTeX RIS

Yangyang Chen, Yi Zhao. 2019-09-15. The normalized Laplacian spectrum and eigentime identities of hype-cubes. https://arxiv.org/abs/1909.06782

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