More on Spectral Analysis of Signed Networks

被引:1
|
作者
Yu, Guihai [1 ]
Qu, Hui [1 ,2 ]
机构
[1] Guizhou Univ Finance & Econ, Sch Math & Stat, Guiyang 550025, Guizhou, Peoples R China
[2] Shandong Coinnovat Ctr Future Intelligent Comp, Yantai 264005, Shandong, Peoples R China
关键词
GRAPH-THEORY; LAPLACIAN EIGENVALUES; NORMALIZED LAPLACIAN; UNICYCLIC GRAPHS; POSITIVE INDEX; INERTIA; NULLITY; ENERGY; BOUNDS;
D O I
10.1155/2018/3467158
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
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.
引用
收藏
页数:6
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