More on spectral analysis of signed networks
type: Item
instance of: scholarly article
title: More on spectral analysis of signed networks
zbMATH Open document ID: 1407.05154
DOI: 10.1155/2018/3467158
author: Guihai Yu
author: Hui Qu
published in: Complexity
publication date: 2019-02-19T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 05C50
Mathematics Subject Classification ID: 05C82
Mathematics Subject Classification ID: 90B10
zbMATH DE Number: 7024894
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/3467158
OpenAlex ID: W2896947499
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description: scientific article; zbMATH DE number 7024894