Degree of a vertex

Definition

Definition for an undirected graph without loops, parallel edges, or weights

Suppose $G$ is an undirected graph and $x$ is a vertex of $G$. The degree or valency of $x$ is defined as the number of vertices of $G$ adjacent to $x$, or equivalently, as the number of edges of $G$ that have $x$ as one of their endpoints. Explicitly, if $V(G)$ and $E(G)$ denote the vertex set and edge set, the degree of $x$ is:

$|\{y\in V(G)\mid \{x,y\}\in E(G)\}|$