Degree of a vertex

Definition

Let $G$ be a graph and let $v$ be a vertex of $G$ with a finite neighbourhood $N(v)$. The degree of $v$ is the number $$\deg(v) = |N(v)|$$ of vertices adjacent to $v$. It is also the number of edges that contain $v$.

Remarks

A vertex of degree $0$ is isolated, and a vertex of degree $1$ is a leaf. A graph is locally finite when each vertex has finite degree. Each finite graph is locally finite. In a multigraph, the degree counts edges with multiplicity, and a loop counts twice.

Explanations

L1 human

The degree of a vertex is the number of edges at that vertex. In a friendship graph it is the number of friends of a person.