Laplacian matrixorientationmodular decompositionWe study the eigenspace with largest eigenvalue of the Laplacian matrix of a simple graph. We find a surprising connection of this space with the theory of modular decomposition of Gallai, whereby eigenvectors can be used to discover modules. In the ...
Eigenvalue Bounds for the Signless $p$-Laplacian We consider the signless $p$-Laplacian $Q_p$ of a graph, a generalisation of the quadratic form of the signless Laplacian matrix (the case $p=2$). In analogy to Rayleigh's principle the minimum and maximum of $Q_p$ on the $p$-norm...
1.We prove thatμ1(T) < max1 andλ1 (T) < max1, whereμ1(T) andλ1(T) are the largest eigenvalue of the Laplacian matrix and the adjacency matrix of T.设δj′= max{dυ:dist(υ,w)=j},j=1,2,…,k-2,我们证明和这里μ1(T)和λ1(T)分别是T的Laplacian矩阵和邻接矩阵的最大...
On the Computation of Dominant Eigenpairs of a Matrix Valued Linear Operator 11 -- 56:43 App Randomized Joint Diagonalization 14 -- 59:24 App Computational Graphs for Matrix Functions 10 -- 1:04:50 App A Not So Simple Matter of Software 20 -- 1:01:20 App 07 - Laplacian solvers ...
14.The Second Largest Eigenvalue of Laplacian Matrix of Tree;树的Laplacian矩阵的第二大特征值 15.Estimate for the Upper Bound of Second Eigenvalue of a Certain Differential Systems;某类微分系统第二特征值的上界估计 16.Each eigenstate of an observable corresponds to an eigenvector of the operator,...
Laplacian matrixAdjacency matrixLargest eigenvalueLet T be a tree with vertex set V . Let d v denotes the degree of v ?ce:hsp sp="0.25"/> V . Let Δ = max{ d v : v ?ce:hsp sp="0.25"/> V }. Let u ?ce:hsp sp="0.25"/> V such that d u = Δ . Let k = e u + ...
Graph Adjacency matrix Signless Laplacian Second largest eigenvalue 1. Introduction Let G=(V(G),E(G)) be a simple graph of order n=|V(G)| and size m=|E(G)|. If an edge e∈E(G) joins vertices u,v∈V(G) then, for short, uv stands for e. The adjacency matrix of G is de...
Let Gbe a connected weighted graph on vertices {1,2,…,n} and L be the Laplacian matrix of GLet μ be the second smallest eigenvalue of L and Y be an eigen... RB Bapat,S Pati - 《Linear & Multilinear Algebra》 被引量: 109发表: 1998年 Realization of consensus of multi-agent syst...
and 2 (LG (x)) denotes the second smallest eigenvalue of the statedependent Laplacian matrix LG (x) with its spectrum ordered as 1 (LG ) 2 (LG ) 1 1 1 n (LG ): Furthermore, we restrict the feasible set of (2) by imposing the proximity constraint dij := kxi 0...
Spectral clustering methods allow datasets to be partitioned into clusters by mapping the input datapoints into the space spanned by the eigenvectors of the Laplacian matrix. In this article, we make use of the incomplete Cholesky decomp... L Rocco,VB Marc,S Johan - 《Entropy》 被引量: 2发...