- Degree matrix
In the mathematical field of graph theory the degree matrix is a diagonal matrix which contains information about the degree of each vertex. It is used together with the adjacency matrix to construct the Laplacian matrix of a graph.
Given a graph G = (V,E) with the degree matrix D for G is a square matrix defined as
Vertex labeled graph Degree matrix
For an undirected graph, the degree of a vertex is the number of edges incident to the vertex. This means that each loop is counted twice. This is because each edge has two endpoints and each endpoint adds to the degree.
- The degree matrix of a k-regular graph has a constant diagonal of k
Wikimedia Foundation. 2010.
Look at other dictionaries:
Matrix decoder — is an audio technology where a finite number of discrete audio channels (e.g., 2) are decoded into a larger number of channels on play back (e.g., 5). The channels are generally, but not always, arranged for transmission or recording by an… … Wikipedia
Matrix exponential — In mathematics, the matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function. Abstractly, the matrix exponential gives the connection between a matrix Lie algebra and the corresponding Lie group.… … Wikipedia
Matrix mechanics — Quantum mechanics Uncertainty principle … Wikipedia
Matrix (mathematics) — Specific elements of a matrix are often denoted by a variable with two subscripts. For instance, a2,1 represents the element at the second row and first column of a matrix A. In mathematics, a matrix (plural matrices, or less commonly matrixes)… … Wikipedia
Matrix difference equation — A matrix difference equation is a difference equation in which the value of a vector (or sometimes, a matrix) of variables at one point in time is related to its own value at one or more previous points in time, using matrices. Occasionally … Wikipedia
Matrix representation of conic sections — In mathematics, the matrix representation of conic sections is one way of studying a conic section, its axis, vertices, foci, tangents, and the relative position of a given point. We can also study conic sections whose axes aren t parallel to our … Wikipedia
Matrix pencil — If are complex matrices for some nonnegative integer l, and (the zero matrix), then the matrix pencil of degree l is the matrix valued function defined on the complex numbers A particular case is a linear matrix pencil … Wikipedia
Degree of a continuous mapping — This article is about the term degree as used in algebraic topology. For other uses, see degree (mathematics). A degree two map of a sphere onto itself. In topology, the degree is a numerical invariant that describes a continuous mapping between… … Wikipedia
Matrix (music) — In music, especially folk and popular music, a matrix is an element of variations which does not change. The term was derived from use in musical writings and from Arthur Koestler s The Act of Creation, who defines creativity as the… … Wikipedia
Laplacian matrix — In the mathematical field of graph theory the Laplacian matrix, sometimes called admittance matrix or Kirchhoff matrix, is a matrix representation of a graph. Together with Kirchhoff s theorem it can be used to calculate the number of spanning… … Wikipedia