The Laplacian spectrum and average trapping time for weighted Dyson hierarchical network

Meifeng Dai, Wenjing Feng, Xianbin Wu, Huijia Chi, Peng Li and Weiyi Su

Physica A: Statistical Mechanics and its Applications, 2019, vol. 515, issue C, 510-518

Abstract: In this paper, we consider the weighted Dyson hierarchical network, that is a weighted fully-connected network, where the pattern of weights is ruled by a weight factor. Given that the Laplacian operator is intrinsically implied in the analysis of dynamic processes occurring on complex networks, Laplacian spectrum allows addressing analytically a large class of problems. Exploiting the deterministic recursive structure, we are able to derive explicitly all eigenvalues and their corresponding eigenvectors of Laplacian matrix. Further, we derive exact solutions of the trapping time (TT) and average trapping time (ATT) on the weighted Dyson hierarchical network with weight-dependent walk. The obtained results show that TT and ATT are related to the weight factor of the weighted Dyson hierarchical network.

Keywords: Weighted Dyson hierarchical network; Laplacian spectrum; Weight-dependent walk; Trapping time; Average trapping time (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:515:y:2019:i:c:p:510-518

DOI: 10.1016/j.physa.2018.09.157

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