Talk:Degree matrix

I'm wondering if the example on a degree matrix is correct. The text states

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.

Vertex 1 in the diagram has two non-loop edges and one loop edge. According to the text this should mean that the degree of vertex 1 is 4. However, in the degree matrix the top-left value is 3.

Am I misunderstanding the definition? -- 203.12.172.254 06:44, 11 January 2007 (UTC)

Looks like someone fixed the example. 67.100.217.179 (talk) 19:03, 7 September 2008 (UTC)

Yes, it is wrong. I fixed it. Alphama (talk) 19:28, 28 October 2020 (UTC)

degree matrix is not the sum of number of edges but the sum of edge-weights

I am wondering if the definition of the degree matrix itself is correct. It is stated that “it is a diagonal matrix which contains information about the degree of each vertex—that is, the number of edges attached to each vertex”, but I think it would be more correct to say that is contains information about the strength of each vertex (given by the sum of the weights of all edges attached to the vertex). Indeed in [1], the degree matrix of a weighted undirected matrix G is defined as a diagonal matrix whose entries are given by the sum of all neighboring link weights. I feel that this definition well generalizes to weighted and binary undirected matrices with positive weights. However, it probably does not generalise to directed matrices and matrices containing negative values. Am I saying something completely wrong?

[1] Ortega, Antonio, Graph Signal Processing: Overview, Challenges, and Applications, Proceedings of the IEEE, 2018 Rigonii (talk) 14:56, 13 April 2023 (UTC)