local degree

The degree of a graph vertex v of a graph G, also called the vertex degree or local degree, is the number of graph edges which touch v. The vertex degrees are illustrated above for a random graph. The vertex degree is also called the local degree or valency. The ordered list of vertex degrees in a given graph is called its degree sequence. A list of vertex degrees of a graph can be computed in the Wolfram Language using VertexDegree[g], and precomputed vertex degrees are available for particular embeddings of many named graphs via GraphData[graph, VertexDegrees]. The minimum vertex degree in a graph G is denoted δ(G), and the maximum vertex degree is denoted Δ(G).

degree sequence | directed graph | even vertex | graph | graph edge | graph vertex | indegree | maximum vertex degree | minimum vertex degree | odd vertex | outdegree | planted tree | Vizing's theorem