Undirected edge

Link

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In graph theory, an undirected edge ^[1][2] is an edge that connects an unordered pair of vertices. Undirected edges are the defining features of an undirected graph. Its counterpart is the directed edge, which connects the same two vertices by assigning a direction from a tail to a head.

Definition

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Definition 1 (Undirected edge)

Let $G=(V,E)$ be a graph with vertex set $V$ and edge set $E$. An undirected edge is an ??unordered pair?? $\{u,v\}\in E$ of vertices $u,v\in V$, where $u$ and $v$ are called endpoints of the edge.

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: $\{a,b\}=\{b,a\}$.

References

1. [1]

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

2. [2]

   “Undirected Edge”, Wolfram MathWorld, Available: https://mathworld.wolfram.com/UndirectedEdge.html, Accessed: 2026-08-27 ↩