Degree (graph theory)

Number of edges touching a vertex in a graph

In graph theory, the degree (or valency) of a vertex of a graph is the number of edges that are incident to the vertex; in a multigraph, a loop contributes 2 to a vertex's degree, for the two ends of the edge. The degree of a vertex v {\displaystyle v} is denoted deg ⁡ ( v) {\displaystyle \deg(v)} or deg ⁡ v {\displaystyle \deg v} . The maximum degree of a graph G {\displaystyle G} is denoted by Δ ( G) {\displaystyle \Delta (G)} , and is the maximum of G {\displaystyle G} 's vertices' degrees.

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