Coherence in a family of tree networks with an application of Laplacian spectrum
Coherence in a family of tree networks with an application of Laplacian spectrum
复制标题
应用拉普拉斯谱的树网络族的相干性
DOI：
10.1063/1.4897568
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发表时间：
2014-12-01
期刊：
影响因子：
2.9
通讯作者：
Chen, Fangyue
中科院分区：
文献类型：
--
作者：
Sun, Weigang;Ding, Qingyan;Chen, Fangyue
本文研究了一类树网络中的一致性问题，研究了用拉普拉斯谱表征的网络相干性的一阶和二阶一致性。根据树的结构，我们得到了拉普拉斯矩阵及其拉普拉斯特征值在两个连续世代的递推关系。然后我们得到了所有非零拉普拉斯本征值的倒数和与平方倒数和的解析表达式。最后，我们计算了一阶和二阶网络相干性，发现一阶和二阶相干性随网络规模N的标度分别为lnN和N，比一些已研究的树形图，如Peano盆地分形图、T图和广义Vicsek分形图要小。(C)2014 AIP出版有限责任公司。
In this paper, we study consensus problems in a family of tree networks and investigate first and second order consensus denoted as network coherence characterized by Laplacian spectrum. According to the tree structures, we obtain the recursive relationships of Laplacian matrix and its Laplacian eigenvalues at two successive generations. We then obtain the analytical expressions for the sum of the reciprocals and the square reciprocals of all nonzero Laplacian eigenvalues. Finally, we calculate first and second order network coherence and see that the scalings of first and second order coherence with network size N are lnN and N, which are smaller than some studied tree graphs, such as Peano basin fractal, T-graph, and generalized Vicsek fractal. (C) 2014 AIP Publishing LLC.