Editing Degree matrix (section)

{{Short description|Type of matrix in algebraic graph theory}}
In the [[mathematics|mathematical]] field of [[algebraic graph theory]], the '''degree matrix''' of an [[undirected graph]] is a [[diagonal matrix]] which contains information about the [[degree (graph theory)|degree]] of each [[vertex (graph theory)|vertex]]—that is, the number of edges attached to each vertex.<ref name="clv">{{citation
 | last1 = Chung | first1 = Fan | author1-link = Fan Chung
 | last2 = Lu | first2 = Linyuan
 | last3 = Vu | first3 = Van | author3-link = Van Vu
 | doi = 10.1073/pnas.0937490100
 | issue = 11
 | journal = Proceedings of the National Academy of Sciences of the United States of America
 | mr = 1982145
 | pages = 6313–6318
 | title = Spectra of random graphs with given expected degrees
 | volume = 100
 | year = 2003 | pmid=12743375 | pmc=164443| bibcode = 2003PNAS..100.6313C | doi-access = free }}.</ref> 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.<ref name="mohar">{{citation
 | last = Mohar | first = Bojan | authorlink = Bojan Mohar
 | editor1-last = Beineke | editor1-first = Lowell W.
 | editor2-last = Wilson | editor2-first = Robin J.
 | contribution = Graph Laplacians
 | isbn = 0-521-80197-4
 | mr = 2125091
 | pages = 113–136
 | publisher = Cambridge University Press, Cambridge
 | series = Encyclopedia of Mathematics and its Applications
 | title = Topics in algebraic graph theory
 | url = https://books.google.com/books?id=z2K26gZLC1MC&pg=PA113
 | volume = 102
 | year = 2004}}.</ref>