Network coherence and eigentime identity on a family of weighted fractal networks
Network coherence and eigentime identity on a family of weighted fractal networks
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加权分形网络族上的网络相干性和特征时间恒等式
DOI：
10.1016/j.chaos.2018.02.020
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发表时间：
2018-04
影响因子：
7.8
通讯作者：
Su Weiyi
中科院分区：
文献类型：
--
作者：
Zong Yue;Dai Meifeng;Wang Xiaoqian;He Jiaojiao;Zou Jiahui;Su Weiyi
网络相干性和特征时间同一性的研究引起了人们的广泛关注。在本文中，一阶网络相干性用权重依赖行走的整个平均首次通过时间（EMFPT）来表征，而特征时间恒等式用所有非零归一化拉普拉斯特征值的倒数和来量化。构造了一个权重因子r （0< r≤1）的加权分形网络族。基于一阶网络相干性与EMFPT的关系，得到了一阶网络相干性的渐近性质。结果表明，一阶相干性随网络大小的缩放随权重因子的取值范围的变化遵循三个规律。第一定律为网络规模N N的幂律函数，当1 s< r≤1时，其指数为log s r；第二定律是，当r= 1 s时，缩放服从（ln N N） 2 N N（即网络大小与网络大小的平方对数之商）；第三定律是当0< r< 1s时，缩放服从ln N N N N（即网络规模与网络规模的对数之商）。因此，当0< r≤1时，加权分形网络的一阶相干度尺度随r的减小而减小。然后，通过计算递归定义的几个小次多项式的根，可以得到所有的非零归一化拉普拉斯特征值。所得结果表明，特征时间恒等式的标度根据权因子的取值范围服从两个规律。第一定律是当0< r≤1且r≠1s时，尺度服从ln N N（即网络大小的对数）；第二定律是当r= 1 s时，缩放服从N N N ln N N（即网络大小与其对数的乘积）。
The study on network coherence and eigentime identity has gained much interest. In this paper, the first-order network coherence is characterized by the entire mean first-passage time (EMFPT) for weight-dependent walk, while the eigentime identity is quantified by the sum of reciprocals of all nonzero normalized Laplacian eigenvalues. We construct a family of weighted fractal networks with the weight factor r (0< r≤ 1). Based on the relationship between the first-order network coherence and the EMFPT, the asymptotic behavior of the first-order network coherence is obtained. The obtained results show that the scalings of first-order coherence with network size obey three laws according to the range of the weight factor. The first law is that the scaling obeys a power-law function of the network size N n with the exponent, represented by log s r, when 1 s< r≤ 1; The second law is that the scaling obeys (ln N n) 2 N n (ie, the quotient of the square logarithm of the network size and the network size), when r= 1 s; The third law is that the scaling obeys ln N n N n (ie, the quotient of the logarithm of the network size and the network size), when 0< r< 1 s. Thus, the scaling of the first-order coherence of weighted fractal networks decreases with the decreasing of r, when 0< r≤ 1. Then, all nonzero normalized Laplacian eigenvalues can be obtained by computing the roots of several small-degree polynomials defined recursively. The obtained results show that the scalings of the eigentime identity obey two laws according to the range of the weight factor. The first law is that the scaling obeys ln N n (ie, the logarithm of the network size), when 0< r≤ 1 and r≠ 1 s; The second law is that the scaling obeys N n ln N n (ie, the product of network size and its logarithm), when r= 1 s.
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影响因子：
4
作者：
Li Deqiong;Hou Yaoping
通讯作者：
Hou Yaoping
网络图中的网络一致性
DOI：
10.1016/j.cnsns.2015.03.011
发表时间：
2015-10
期刊：
Communications in Nonlinear Science & Numerical Simulation
影响因子：
--
作者：
Ding, Qingyan;Sun, Weigang;Chen, Fangyue
通讯作者：
Chen, Fangyue
影响因子：
1.3
作者：
Y. Mao
通讯作者：
Y. Mao
DOI：
10.1109/ecc.2015.7330605
发表时间：
2014-11
期刊：
2015 European Control Conference (ECC)
影响因子：
--
作者：
T. Summers;I. Shames;J. Lygeros;F. Dörfler
通讯作者：
T. Summers;I. Shames;J. Lygeros;F. Dörfler
影响因子：
2.9
作者：
Sun, Weigang;Ding, Qingyan;Chen, Fangyue
通讯作者：
Chen, Fangyue