cycle in a simple graph
圈
Meaning in context
In a simple graph, a cycle consists of distinct vertices v_1,…,v_k with k ≥ 3, consecutive pairs joined, and v_k joined to v_1; its length is k.
简单图中的圈由至少三个互不相同的顶点依次连接而成，最后一个顶点再与第一个相连；长度为顶点数，也为边数。
Example
The three edges form a cycle of length three.
Usage and distinctions
Traversing an edge and immediately returning does not form a cycle in a simple graph; reversing or rotating a traversal describes the same underlying cycle.
Recommended reading in this subject · Preparation & skip guidance
Definition sources
- Keller and Trotter — Applied Combinatorics (2016)Section 5.1, cycle definition and length convention · Checked 2026-10-14
Translation sources
- Reinhard Diestel — 图论，第五版，官方中文目录目录，§1.3「路和圈」（中文名称证据，仅目录） · Checked 2026-10-14