Degree matrix

In the mathematical field of algebraic graph theory, the degree matrix of an undirected graph is a diagonal matrix which contains information about the degree of each vertex—that is, the number of edges attached to each vertex.^[1] It is used together with the adjacency matrix to construct the Laplacian matrix of a graph: the Laplacian matrix is the difference of the degree matrix and the adjacency matrix.^[2]

^ Chung, Fan; Lu, Linyuan; Vu, Van (2003), "Spectra of random graphs with given expected degrees", Proceedings of the National Academy of Sciences of the United States of America, 100 (11): 6313–6318, Bibcode:2003PNAS..100.6313C, doi:10.1073/pnas.0937490100, MR 1982145, PMC 164443, PMID 12743375.
^ Mohar, Bojan (2004), "Graph Laplacians", in Beineke, Lowell W.; Wilson, Robin J. (eds.), Topics in algebraic graph theory, Encyclopedia of Mathematics and its Applications, vol. 102, Cambridge University Press, Cambridge, pp. 113–136, ISBN 0-521-80197-4, MR 2125091.