Optimizing the Coherence of a Network of Networks

Mackin, Erika; Patterson, Stacy

doi:10.1109/tcns.2020.2979884

Cited by 7 publications

(3 citation statements)

References 35 publications

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“…where K is the projection operator, K I − 1 s 11 T , and 1 is the svector of all nodes. H (1) is given by the H 2 norm of the systems defined in Eqs 1 and 3.…”

Section: Network Coherencementioning

confidence: 99%

“…The Kirchhoff index (Kf) is also closely related to the nonzero eigenvalues of the Laplacian matrix L, Kf s s i 2 1 λi 2s 2 H (1) .…”

Section: Network Coherencementioning

confidence: 99%

“…With the development of network science, the research of complex networks has been extended to many fields, such as technical networks and transportation networks. Nowadays, the relevant theoretical knowledge of complex networks has been widely used in physics, computer science, life science, and other fields, such as consensus [1][2][3][4][5], resistance distance and Kirchhoff index [6], robustness [7,8], and network synchronization [9,10].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Consensus analysis of the weighted corona networks

Zhu

Gao³

et al. 2022

Front. Phys.

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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 G1◦G2, this study gives different weights to the edges of G1◦G2 to obtain the weighted corona networks G̃1◦G̃2 and studies the consensus of G̃1◦G̃2. The consensus of the networks can be measured by coherence. First, the Laplacian polynomial of G̃1◦G̃2 is derived by using the properties of an orthogonal matrix. Second, the relationship between the first-order coherence of G̃1◦G̃2 and G1 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.

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“…where K is the projection operator, K I − 1 s 11 T , and 1 is the svector of all nodes. H (1) is given by the H 2 norm of the systems defined in Eqs 1 and 3.…”

Section: Network Coherencementioning

confidence: 99%

“…The Kirchhoff index (Kf) is also closely related to the nonzero eigenvalues of the Laplacian matrix L, Kf s s i 2 1 λi 2s 2 H (1) .…”

Section: Network Coherencementioning

confidence: 99%