Bidirected edge

In graph theory, a bidirected edge ^[1] is a pair of directed edges $(u,v)$ and $(v,u)$ joining the same two vertices $u$ and $v$ in opposite directions. Bidirected edges are used to represent an undirected edge within a directed graph, since either endpoint can then reach the other.

Definition

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Definition 1 (Bidirected edge)

Let $G=(V,E)$ be a directed graph with vertex set $V$ and edge set $E$. Two vertices $u,v\in V$ are joined by a bidirected edge if

$$(u,v)\in E\wedge (v,u)\in E$$

that is, if both directed edges between $u$ and $v$ belong to $E$.

References

1. [1]

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