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- Title
Coherence analysis of a family of weighted star-composed networks.
- Authors
Dai, Meifeng; Ju, Tingting; Hou, Yongbo; Chang, Jianwei; Sun, Yu; Su, Weiyi
- Abstract
Recently, the study of many kinds of weighted networks has received the attention of researchers in the scientific community. In this paper, first, a class of weighted star-composed networks with a weight factor is introduced. We focus on the network consistency in linear dynamical system for a class of weighted star-composed networks. The network consistency can be characterized as network coherence by using the sum of reciprocals of all nonzero Laplacian eigenvalues, which can be obtained by using the relationship of Laplacian eigenvalues at two successive generations. Remarkably, the Laplacian matrix of the class of weighted star-composed networks can be represented by the Kronecker product, then the properties of the Kronecker product can be used to obtain conveniently the corresponding characteristic roots. In the process of finding the sum of reciprocals of all nonzero Laplacian eigenvalues, the key step is to obtain the relationship of Laplacian eigenvalues at two successive generations. Finally, we obtain the main results of the first- and second-order network coherences. The obtained results show that if the weight factor is 1 then the obtained results in this paper coincide with the previous results on binary networks, otherwise the scalings of the first-order network coherence are related to the node number of attaching copy graph, the weight factor and generation number. Surprisingly, the scalings of the first-order network coherence are independent of the node number of initial graph. Consequently, it will open up new perspectives for future research.
- Subjects
LAPLACIAN matrices; KRONECKER products; LINEAR dynamical systems; SCIENTIFIC community; BINARY codes
- Publication
International Journal of Modern Physics B: Condensed Matter Physics; Statistical Physics; Applied Physics, 2019, Vol 33, Issue 23, pN.PAG
- ISSN
0217-9792
- Publication type
Article
- DOI
10.1142/S0217979219502643