HOU Yaoping,LI Jiongsheng,PAN Yongliang.On the Laplacian Eigenvalues of Signed Graphs[J].Linear Multilinear Algebra,2003,51(1):413-423.Y. P. Hou, J. S. Li, and Y. Pan. On the Laplacian eigenvalues of signed graphs. Linear and Multilinear Algebra, 1(51):21-30, 2003....
A signed graph is a graph with a sign attached to each edge. This article extends some fundamental concepts of the Laplacian matrices from graphs to signed graphs. In particular, the largest Laplacian eigenvalue of a signed graph is investigated, which generalizes the corresponding results on the...
这个值是non-negative的,侧面说明Laplacian matrix is positive semi-definite。 2.4.2 The Eigenvalues and Eigenvectors of the Laplacian Matrix Theorem 2.30拉普拉斯矩阵特征值非负 Theorem 2.31拉普拉斯矩阵为0的特征值数量对应于图上连通分量的个数。(使用反证法,用到拉普拉斯矩阵的半正定性质) 2.5 Graph Signal Pr...
By assigning a probability measure via the spectrum of the normalized Laplacian to each graph and using Lp Wasserstein distances between probability measures, we define the corresponding spectral distances dp on the set of all graphs. This approach can even be extended to measuring the distances betw...
For the agents described by a structurally balanced signed digraph, the asymmetric bipartite consensus objective is firstly defined, assigning the agents’ output to different signs and module values. Considering with the completely unknown dynamics of the agents, a novel event-triggered model-free ...
A slicing approach on Riemannian manifolds based on eigenfunctions of the Laplacian was proposed in [66]. OT on the sphere has been intensely studied, e.g., the computation of Wasserstein barycenters [69, 70], the regularity of optimal maps [48], isometric rigidity of Wasserstein spaces [29...
The energy (G) of a graph is the sum of absolute values of the eigenvalues of its adjacency matrix. The matching number \mu(G) is the number of edges in a maximum matching. For a connected graph of order with largest vertex degree Δ≥ 6 we present two new upper bounds for the ener...
In follow-up work, they also built an almost tight wavelet frame based on the polynomial filters [35]. In [34], Shuman et al. proposed filters adapted to the distribution of graph Laplacian eigenvalues, leading to atoms with better discriminatory power. Inspired by the first-order spline ...
All eigenvalues of its signed Laplacian matrix have nonnegative real parts and 0 is a simple eigenvalue. Lemma 2 [28] Suppose that directed signed graph\(\mathcal {G}(A)\)has a spanning tree and structurally balanced. If all nodes of\(\mathcal {G}(A)\)can be partitioned into two ...
Massless modes are therefore described by the kernels of the Laplacians ∆, ∆¯ or equivalently by closed and co-closed forms with respect to the operators in (2.35) D¯χ = 0 , Dψ = 0 , D¯†χ = 0 D†ψ = 0 . (2.39) By the BPS equations the co-boundary ...