Degree Matrix - Example

Example

Vertex labeled graph Degree matrix
\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}

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

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