翻訳と辞書 Words near each other ・ Laplace pressure ・ Laplace principle (large deviations theory) ・ Laplace transform ・ Laplace transform applied to differential equations ・ Laplace's demon ・ Laplace's equation ・ Laplace's law ・ Laplace's method ・ LaPlace, Louisiana ・ Laplace-P ・ LaplacesDemon ・ Laplace–Beltrami operator ・ Laplace–Carson transform ・ Laplace–Runge–Lenz vector ・ Laplace–Stieltjes transform ・ Laplacian matrix ・ Laplacian of the indicator ・ Laplacian smoothing ・ Laplae District ・ Laplanche ・ LaPlanche Street ・ Lapland ・ Lapland (album) ・ Lapland (electoral district) ・ Lapland (Finland) ・ Lapland (former province of Finland) ・ Lapland (Sweden) ・ Lapland Air Command ・ Lapland Air Defence Battallion ・ Lapland Biosphere Reserve Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Laplacian matrix ： ウィキペディア英語版 Laplacian matrix In the mathematical field of graph theory, the Laplacian matrix, sometimes called admittance matrix, Kirchhoff matrix or discrete Laplacian, is a matrix representation of a graph. Together with Kirchhoff's theorem, it can be used to calculate the number of spanning trees for a given graph. The Laplacian matrix can be used to find many other properties of the graph. Cheeger's inequality from Riemannian geometry has a discrete analogue involving the Laplacian matrix; this is perhaps the most important theorem in spectral graph theory and one of the most useful facts in algorithmic applications. It approximates the sparsest cut of a graph through the second eigenvalue of its Laplacian. ==Definition== Given a simple graph ''G'' with ''n'' vertices, its Laplacian matrix $L\_$ is defined as: : $$ L = D - A, where ''D'' is the degree matrix and ''A'' is the adjacency matrix of the graph. In the case of directed graphs, either the indegree or outdegree might be used, depending on the application. The elements of $L$ are given by : $L\_:=$ \begin \deg(v_i) & \mbox\ i = j \\ -1 & \mbox\ i \neq j\ \mbox\ v_i \mbox v_j \\ 0 & \mbox \end where deg(''vi'') is degree of the vertex ''i''. The symmetric normalized Laplacian matrix is defined as:〔 : $$ L^ L D^= I - D^ A D^, The elements of $L^\}\_:=$ \begin 1 & \mbox\ i = j\ \mbox\ \deg(v_i) \neq 0\\ -\frac\ i \neq j\ \mbox\ v_i \mbox v_j \\ 0 & \mbox. \end The random-walk normalized Laplacian matrix is defined as: : $L^L\; =\; I\; -\; D^A$ The elements of $L^\}\_:=$ \begin 1 & \mbox\ i = j\ \mbox\ \deg(v_i) \neq 0\\ -\frac & \mbox\ i \neq j\ \mbox\ v_i \mbox v_j \\ 0 & \mbox. \end 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Laplacian matrix」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.