More on Spectral Analysis of Signed Networks
Spectral graph theory plays a key role in analyzing the structure of social (signed) networks. In this paper we continue to study some properties of (normalized) Laplacian matrix of signed networks. Sufficient and necessary conditions for the singularity of Laplacian matrix are given. We determine t...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2018/3467158 |
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| _version_ | 1832551474212634624 |
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| author | Guihai Yu Hui Qu |
| author_facet | Guihai Yu Hui Qu |
| author_sort | Guihai Yu |
| collection | DOAJ |
| description | Spectral graph theory plays a key role in analyzing the structure of social (signed) networks. In this paper we continue to study some properties of (normalized) Laplacian matrix of signed networks. Sufficient and necessary conditions for the singularity of Laplacian matrix are given. We determine the correspondence between the balance of signed network and the singularity of its Laplacian matrix. An expression of the determinant of Laplacian matrix is present. The symmetry about 1 of eigenvalues of normalized Laplacian matrix is discussed. We determine that the integer 2 is an eigenvalue of normalized Laplacian matrix if and only if the signed network is balanced and bipartite. Finally an expression of the coefficient of normalized Laplacian characteristic polynomial is present. |
| format | Article |
| id | doaj-art-939e20ce5c8e4628bf0f708409749388 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-939e20ce5c8e4628bf0f7084097493882025-02-03T06:01:24ZengWileyComplexity1076-27871099-05262018-01-01201810.1155/2018/34671583467158More on Spectral Analysis of Signed NetworksGuihai Yu0Hui Qu1School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang, Guizhou, 550025, ChinaSchool of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang, Guizhou, 550025, ChinaSpectral graph theory plays a key role in analyzing the structure of social (signed) networks. In this paper we continue to study some properties of (normalized) Laplacian matrix of signed networks. Sufficient and necessary conditions for the singularity of Laplacian matrix are given. We determine the correspondence between the balance of signed network and the singularity of its Laplacian matrix. An expression of the determinant of Laplacian matrix is present. The symmetry about 1 of eigenvalues of normalized Laplacian matrix is discussed. We determine that the integer 2 is an eigenvalue of normalized Laplacian matrix if and only if the signed network is balanced and bipartite. Finally an expression of the coefficient of normalized Laplacian characteristic polynomial is present.http://dx.doi.org/10.1155/2018/3467158 |
| spellingShingle | Guihai Yu Hui Qu More on Spectral Analysis of Signed Networks Complexity |
| title | More on Spectral Analysis of Signed Networks |
| title_full | More on Spectral Analysis of Signed Networks |
| title_fullStr | More on Spectral Analysis of Signed Networks |
| title_full_unstemmed | More on Spectral Analysis of Signed Networks |
| title_short | More on Spectral Analysis of Signed Networks |
| title_sort | more on spectral analysis of signed networks |
| url | http://dx.doi.org/10.1155/2018/3467158 |
| work_keys_str_mv | AT guihaiyu moreonspectralanalysisofsignednetworks AT huiqu moreonspectralanalysisofsignednetworks |