When.com Web Search

  1. Ad

    related to: laplacian matrix vertex method pdf sample paper chemistry class 11

Search results

  1. Results From The WOW.Com Content Network
  2. Laplacian matrix - Wikipedia

    en.wikipedia.org/wiki/Laplacian_matrix

    A vertex with a large degree, also called a heavy node, results in a large diagonal entry in the Laplacian matrix dominating the matrix properties. Normalization is aimed to make the influence of such vertices more equal to that of other vertices, by dividing the entries of the Laplacian matrix by the vertex degrees.

  3. Spectral clustering - Wikipedia

    en.wikipedia.org/wiki/Spectral_clustering

    The general approach to spectral clustering is to use a standard clustering method (there are many such methods, k-means is discussed below) on relevant eigenvectors of a Laplacian matrix of . There are many different ways to define a Laplacian which have different mathematical interpretations, and so the clustering will also have different ...

  4. Spectral graph theory - Wikipedia

    en.wikipedia.org/wiki/Spectral_graph_theory

    The famous 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.

  5. Algebraic connectivity - Wikipedia

    en.wikipedia.org/wiki/Algebraic_connectivity

    The algebraic connectivity (also known as Fiedler value or Fiedler eigenvalue after Miroslav Fiedler) of a graph G is the second-smallest eigenvalue (counting multiple eigenvalues separately) of the Laplacian matrix of G. [1] This eigenvalue is greater than 0 if and only if G is a connected graph. This is a corollary to the fact that the number ...

  6. Discrete Laplace operator - Wikipedia

    en.wikipedia.org/wiki/Discrete_Laplace_operator

    In mathematics, the discrete Laplace operator is an analog of the continuous Laplace operator, defined so that it has meaning on a graph or a discrete grid.For the case of a finite-dimensional graph (having a finite number of edges and vertices), the discrete Laplace operator is more commonly called the Laplacian matrix.

  7. Degree matrix - Wikipedia

    en.wikipedia.org/wiki/Degree_matrix

    In the mathematical field of algebraic graph theory, the degree matrix of an undirected graph is a diagonal matrix which contains information about the degree of each vertex—that is, the number of edges attached to each vertex. [1]

  8. Eigenvalues and eigenvectors - Wikipedia

    en.wikipedia.org/wiki/Eigenvalues_and_eigenvectors

    Such a matrix A is said to be similar to the diagonal matrix Λ or diagonalizable. The matrix Q is the change of basis matrix of the similarity transformation. Essentially, the matrices A and Λ represent the same linear transformation expressed in two different bases. The eigenvectors are used as the basis when representing the linear ...

  9. Expander graph - Wikipedia

    en.wikipedia.org/wiki/Expander_graph

    Here one considers the matrix ⁠ 1 / d ⁠ A, which is the Markov transition matrix of the graph G. Its eigenvalues are between −1 and 1. For not necessarily regular graphs, the spectrum of a graph can be defined similarly using the eigenvalues of the Laplacian matrix.