2014
DOI: 10.1142/s0129183114500375
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Random walk and first passage time on a weighted hierarchical network

Abstract: This paper reports a weighted hierarchical network generated on the basis of self-similarity, in which each edge is assigned a different weight in the same scale. We studied two substantial properties of random walk: the first-passage time (FPT) between a hub node and a peripheral node and the FPT from a peripheral node to a local hub node over the network. Meanwhile, an analytical expression of the average sending time (AST) is deduced, which reflects the average value of FPT from a hub node to any other node… Show more

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Cited by 11 publications
(4 citation statements)
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“…Gujun Wang popularized the fan graph spanning tree and applied it to the iterative Apollonian networks. He assigned weight A to edges between two outer vertices of the wheel graph and weight B to edges between center vertex and one outer vertex, thereby calculating the number of weighted wheel graph spanning trees [11], [12] and the weighted wheel graph spanning trees has widely used in random walks [13].…”
Section: [F(n)] [W(n)]mentioning
confidence: 99%
“…Gujun Wang popularized the fan graph spanning tree and applied it to the iterative Apollonian networks. He assigned weight A to edges between two outer vertices of the wheel graph and weight B to edges between center vertex and one outer vertex, thereby calculating the number of weighted wheel graph spanning trees [11], [12] and the weighted wheel graph spanning trees has widely used in random walks [13].…”
Section: [F(n)] [W(n)]mentioning
confidence: 99%
“…Spanning tree is an important concept in many fields, including Computer science and Fractal geometry [1]. In the meantime, it has a deep relationship with many aspects of network, such as transportation [2], reliability [3], random walks [4], and optimal Synchronization [5]. Furthermore, the problem of counting spanning trees has been associated with other interesting problems, including origin of fractality in complex networks [6], Potts model [7] and dimer coverings [8].…”
Section: Introductionmentioning
confidence: 99%
“…In view of the fact that many research studies on random walks mainly focus on undirected and unweighted networks, Zhang et al [14] discussed two types of random walks for a class of weighted and undirected networks. Dai et al [15][16][17][18] introduced several weighted random walks on the complex network. In fact, many real networks contain the relationships between individuals with different weights in different directions.…”
Section: Introductionmentioning
confidence: 99%