Average weighted trapping time of the node- and edge-weighted fractal networks
Average weighted trapping time of the node- and edge-weighted fractal networks
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节点加权和边加权分形网络的平均加权捕获时间
DOI：
10.1016/j.cnsns.2016.03.001
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发表时间：
2016
影响因子：
3.9
通讯作者：
Su Weiyi
中科院分区：
文献类型：
--
作者：
Dai Meifeng;Ye D;an;Hou Jie;Xi Lifeng;Su Weiyi
在本文中，我们研究了节点和边加权分形网络的陷阱问题与潜在的几何形状，专注于一个特殊的情况下，一个完美的陷阱位于中心节点。我们导出了平均加权捕获时间（AWTT）的精确解析公式，即整个网络上节点到陷阱的平均加权首达时间的平均值，它与网络规模Ng、副本数s、节点权重因子w和边权重因子r有关.结果表明，在大型网络中，当srw2 ≥ 1时，AWTT随网络规模Ng的幂律增长，其指数为θ（s，r，w）= logs（srw2）.特别是当srw2 = 1时，AWTT随阶数Ng的增加而增加，并与log Ng成正比.这也意味着捕获过程的效率取决于三个主要参数：副本数s> 1，节点权重因子0< w≤ 1，边缘权重因子0< r≤ 1。srw 2的值越小，捕集过程的效率越高。
In this paper, we study the trapping problem in the node-and edge-weighted fractal networks with the underlying geometries, focusing on a particular case with a perfect trap located at the central node. We derive the exact analytic formulas of the average weighted trapping time (AWTT), the average of node-to-trap mean weighted first-passage time over the whole networks, in terms of the network size N g, the number of copies s, the node-weight factor w and the edge-weight factor r. The obtained result displays that in the large network, the AWTT grows as a power-law function of the network size N g with the exponent, represented by θ (s, r, w)= log s (s r w 2) when srw 2≠ 1. Especially when s r w 2= 1, AWTT grows with increasing order N g as log N g. This also means that the efficiency of the trapping process depend on three main parameters: the number of copies s> 1, node-weight factor 0< w≤ 1, and edge-weight factor 0< r≤ 1. The smaller the value of srw 2 is, the more efficient the trapping process is.