structural:expansion, linguistic:voice_change, information:classification
Definition

Given a graph G = (V, E) {\displaystyle G=(V,E)} with | V | = n {\displaystyle |V|=n}, the degree matrix D {\displaystyle D} for G {\displaystyle G} is a n × n {\displaystyle n\times n} diagonal matrix defined as

where the degree deg (v i) {\displaystyle \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 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).