Cycle (Graph)

Definition

Cycle

Let $G=(V,E)$ be an undirected graph. A cycle is a sequence

$$C=(v_0,v_1,\dots ,v_{k-1},v_0),k\ge 3,$$

where $v_0,\dots ,v_{k-1}$ are pairwise distinct vertices and

$$\{v_i,v_{i+1}\}\in E(0\le i<k),$$

with indices taken modulo $k$, so $v_k=v_0$. Thus, the sequence follows edges from its starting vertex back to itself without visiting any other vertex twice.