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Degree matrix : ウィキペディア英語版
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—that is, the number of edges attached to each vertex.〔.〕 It is used together with the adjacency matrix to construct the Laplacian matrix of a graph.〔.〕
==Definition==
Given a graph G=(V,E) with |V|=n the degree matrix D for G is a n \times n diagonal matrix defined as〔
:d_:=\left\\ i = j \\
0 & \mbox
\end
\right.

where the degree \deg(v_i) of a vertex counts the number of times an edge terminates at that vertex. In an undirected graph, this means that each new loop increases the degree of a vertex by two. In a directed graph, the term ''degree'' may refer either to indegree (the number of incoming edges at each vertex) or outdegree (the number of outgoing edges at each vertex).

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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