Undirected edge

In graph theory, an undirected edge ^[1] is an edge that connects two vertices symmetrically, without distinguishing one as a source and the other as a target. Undirected edges are the defining feature of an undirected graph, as opposed to the directed edge of a directed graph.

Definition

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Definition 1 (Undirected edge)

Let $G$ be a graph with vertex set $V$. An undirected edge is an unordered pair $\{u,v\}$ of vertices $u,v\in V$; that is, $\{u,v\}=\{v,u\}$.

Notation

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An undirected edge joining $u$ and $v$ is written $\{u,v\}$, or simply $uv$ when no ambiguity arises. Unlike the directed edge $(u,v)$, the order of $u$ and $v$ carries no meaning.

References

1. [1]

   “Glossary of graph theory”, Wikipedia, Available: https://en.wikipedia.org/wiki/Glossary_of_graph_theory, Accessed: 2026-07-14 ↩