Topologies and Laplacian spectra of a deterministic uniform recursive tree

Details Topologies and Laplacian spectra of a deterministic uniform recursive tree Topologies and Laplacian spectra of a deterministic uniform recursive tree

2008-01-27

arxiv.org/abs/0801.4128v2

Eur. Phys. J. B 63, 507-513 (2008).

Physics

Condensed Matter

Statistical Mechanics

7 pages, 1 figures, definitive version accepted for publication in EPJB

Scientific paper

10.1140/epjb/e2008-00262-2

The uniform recursive tree (URT) is one of the most important models and has been successfully applied to many fields. Here we study exactly the topological characteristics and spectral properties of the Laplacian matrix of a deterministic uniform recursive tree, which is a deterministic version of URT. Firstly, from the perspective of complex networks, we determine the main structural characteristics of the deterministic tree. The obtained vigorous results show that the network has an exponential degree distribution, small average path length, power-law distribution of node betweenness, and positive degree-degree correlations. Then we determine the complete Laplacian spectra (eigenvalues) and their corresponding eigenvectors of the considered graph. Interestingly, all the Laplacian eigenvalues are distinct.

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