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Encyclopedia > 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. Mathematics is often defined as the study of topics such as quantity, structure, space, and change. ... A graph diagram of a graph with 6 vertices and 7 edges. ... In linear algebra, a diagonal matrix is a square matrix in which the entries outside the main diagonal are all zero. ... In the mathematical field of graph theory the degree or valency of a vertex v is the number of edges incident to v (with loops being counted twice). ... This article just presents the basic definitions. ...


Definition

Given a graph G = (V,E) with |V|=n the degree matrix D for G is a n times n square matrix defined as For the square matrix section, see square matrix. ...

d_{i,j}:=left{ begin{matrix} deg(v_i) & mbox{if} i = j  0 & mbox{otherwise} end{matrix} right.

Examples

The degree matrix for the following vertex labeled graph In the mathematical discipline of graph theory, a graph labeling is the assignment of unique identifiers to the edges and vertices of a graph. ...

image:6n-graph2.png

is Image File history File links 6n-graph2. ...

begin{pmatrix} 4 & 0 & 0 & 0 & 0 & 0 0 & 3 & 0 & 0 & 0 & 0 0 & 0 & 2 & 0 & 0 & 0 0 & 0 & 0 & 3 & 0 & 0 0 & 0 & 0 & 0 & 3 & 0 0 & 0 & 0 & 0 & 0 & 1 end{pmatrix}.
  • The degree matrix of a k-regular graph has a constant diagonal of k

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