Definition

It is a Graph where the edges form a circle. That is, if we follow ever edge, we should return at the starting node.

If vertices $v_{1}, v_{2}, \dots, v_{n}$ then the edges are $(v_{1}, v_{2}), (v_{2}, v_{3}), \dots, (v_{n - 1}, v_{n}), (v_{n}, v_{1})$ .
They are always $2 -$ regular.
$∣ E ∣ = 2 n /2 = n$

graph LR
    A((A)) o--o B((B))
    B o---o C((C))
    C o---o D((D))
    D o---o A

It is a Walk that starts and ends at the same vertex, but does not repeat vertices.