Cycle

Definition

Let $G$ be a graph. A cycle in $G$ is a circuit $(w_0, w_1, \dots, w_k)$ whose vertices $w_1, \dots, w_k$ are pairwise distinct.

Remarks

The only repeated vertex is $w_0 = w_k$. In a simple graph, each cycle has length $k \ge 3$. The vertices and edges of a cycle of length $k$ form a subgraph isomorphic to the cycle graph $C_k$. A graph with no cycle is acyclic.

Explanations

L1 human

A cycle is a round trip that visits each of its vertices once and comes back to the start. A triangle is the shortest possible cycle in a simple graph.