Edge set

Definition

Let $G$ be a graph with vertex set $V$ and adjacency relation $\sim$. The edge set of $G$ is the set $$E(G) = \{ \{u, v\} : u, v \in V,\ u \sim v \}$$ of unordered pairs of adjacent vertices.

Remarks

Each edge is a $2$-element subset of $V$, because $\sim$ is irreflexive. The number of edges $|E(G)|$ is the size of $G$, and the number of vertices $|V|$ is its order. The handshaking lemma relates $|E(G)|$ to the degrees of the vertices.

Explanations

L1 human

The edge set is the list of all lines of the graph, with each line given by its two end points. A triangle on the vertices $a, b, c$ has the edge set $\{\{a, b\}, \{b, c\}, \{a, c\}\}$.