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More on Spectral Analysis of Signed Networks

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Listed:
  • Guihai Yu
  • Hui Qu

Abstract

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 of eigenvalues of normalized Laplacian matrix is discussed. We determine that the integer 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.

Suggested Citation

  • Guihai Yu & Hui Qu, 2018. "More on Spectral Analysis of Signed Networks," Complexity, Hindawi, vol. 2018, pages 1-6, October.
    • Handle: RePEc:hin:complx:3467158
    DOI: 10.1155/2018/3467158
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    References listed on IDEAS

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    1. Yu, Guihai & Qu, Hui & Tu, Jianhua, 2015. "Inertia of complex unit gain graphs," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 619-629.
    2. Yu, Guihai & Liu, Xin & Qu, Hui, 2017. "Singularity of Hermitian (quasi-)Laplacian matrix of mixed graphs," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 287-292.
    3. Lang, Rongling & Li, Tao & Mo, Desen & Shi, Yongtang, 2016. "A novel method for analyzing inverse problem of topological indices of graphs using competitive agglomeration," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 115-121.
    4. Yu Liu & Lihua You, 2014. "Further Results on the Nullity of Signed Graphs," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-8, February.
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