The degree of a vertex V of a graph is the number of edges ending at V. (If loops are allowed, each loop joining v to itself contributes two to the degree of V.)

In the first graph, the vertices U, V, W and X have degrees 2, 2, 3 and 1. The second graph has vertices V₁, V₂, V₃ and V₄ with degrees 5, 4, 6 and 5.

A graph

A multigraph