Consensus analysis of the weighted corona networks

The consensus of complex networks has attracted the attention of many scholars. The graph operation is a common method to construct complex networks, which is helpful in studying the consensus of complex networks. Based on the corona networks G 1 ◦ G 2 , this study gives different weights to the edg...

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Bibliographic Details
Published in:Frontiers in physics 2022-08, Vol.10
Main Authors: Du, Weiwei, Zhu, Jian, Gao, Haiping, Li, Xianyong
Format: Article
Language:English
Subjects:
consensus
corona operation
first-order coherence
join operation
weighted
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Summary:The consensus of complex networks has attracted the attention of many scholars. The graph operation is a common method to construct complex networks, which is helpful in studying the consensus of complex networks. Based on the corona networks G 1 ◦ G 2 , this study gives different weights to the edges of G 1 ◦ G 2 to obtain the weighted corona networks G ̃ 1 ◦ G ̃ 2 and studies the consensus of G ̃ 1 ◦ G ̃ 2 . The consensus of the networks can be measured by coherence. First, the Laplacian polynomial of G ̃ 1 ◦ G ̃ 2 is derived by using the properties of an orthogonal matrix. Second, the relationship between the first-order coherence of G ̃ 1 ◦ G ̃ 2 and G 1 is deduced by using the relevant properties of the determinant and the conclusion of polynomial coefficients and the principal minors of the matrix. Third, the join operation is introduced to further simplify the analytical formula of network coherence. Finally, a specific network example is used to verify the validity of the conclusion.
ISSN:2296-424X
2296-424X
DOI:10.3389/fphy.2022.948247