Circuit

Definition

Let $G$ be a graph. A circuit in $G$ is a closed trail of positive length. That is a walk $(w_0, w_1, \dots, w_k)$ with $k \ge 1$, $w_k = w_0$, and pairwise distinct edges.

Remarks

A circuit may visit a vertex more than once. A cycle is a circuit with no repeated vertex other than the start. In a simple graph each circuit has length at least $3$. Some authors use the word circuit for a cycle. Others use the word tour.

Explanations

L1 human

A circuit is a trail that ends where it starts. It is a round trip that never uses the same edge twice.