Vertex degree

In an undirected graph, the degree of a vertex $v$ is the number of edges incident to $v$. If there are loops (edges that start and end at $v$), each loop counts as two towards the degree.

Important properties

• The sum of the degrees of all vertices in a graph equals twice the number of edges.

• A vertex of degree 0 is called an isolated vertex.

• A vertex of degree 1 is called a leaf (in trees).