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第1行：
第1行： − + 第7行：
第7行： − 在图论中，图中的一个环是非空轨迹，其中唯一重复的顶点是第一个和最后一个顶点。有向图中的有向环是非空有向迹线，其中唯一重复的顶点是第一个和最后一个顶点。+ 第15行：
第15行： − 不带有环的图称为无环图。不带有有向环的有向图称为有向无环图。没有环的连接图称为树。+ 第29行：
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无编辑摘要
此词条由Jie翻译。
此词条由Jie翻译。
[[文件:Graph cycle.svg|200px|thumb|left|这是一个经过着色的图，用于说明路径H-A-B（绿色），闭合路径或具有重复顶点的路径B-D-E-F-D-C-B（蓝色）和无重复边或顶点的环H-D-G-H（红色）。]]
[[文件:Graph cycle.svg|200px|thumb|right|这是一个经过着色的图，用于说明路径H-A-B（绿色），闭合路径或具有重复顶点的路径B-D-E-F-D-C-B（蓝色）和无重复边或顶点的环H-D-G-H（红色）。]]
In [[graph theory]], a '''cycle''' in a [[Graph (discrete mathematics)|graph]] is a non-empty [[Path (graph theory)#Walk, trail, path|trail]] in which the only repeated [[Vertex (graph theory)|vertices]] are the first and last vertices. A '''directed cycle''' in a [[directed graph]] is a non-empty [[Path (graph theory)#Directed walk, trail, path|directed trail]] in which the only repeated vertices are the first and last vertices.
In [[graph theory]], a '''cycle''' in a [[Graph (discrete mathematics)|graph]] is a non-empty [[Path (graph theory)#Walk, trail, path|trail]] in which the only repeated [[Vertex (graph theory)|vertices]] are the first and last vertices. A '''directed cycle''' in a [[directed graph]] is a non-empty [[Path (graph theory)#Directed walk, trail, path|directed trail]] in which the only repeated vertices are the first and last vertices.
In graph theory, a cycle in a graph is a non-empty trail in which the only repeated vertices are the first and last vertices. A directed cycle in a directed graph is a non-empty directed trail in which the only repeated vertices are the first and last vertices.
In graph theory, a cycle in a graph is a non-empty trail in which the only repeated vertices are the first and last vertices. A directed cycle in a directed graph is a non-empty directed trail in which the only repeated vertices are the first and last vertices.
在图论中，一个图中的环Cycle是一个非空轨迹，其中唯一重复的点是起始点和最终点。如果是一个有向图的有向环Directed cycle，它同样是非空有向迹线，其中唯一重复的点也是起始点和最终点。
A graph without cycles is called an acyclic graph. A directed graph without directed cycles is called a directed acyclic graph. A connected graph without cycles is called a tree.
A graph without cycles is called an acyclic graph. A directed graph without directed cycles is called a directed acyclic graph. A connected graph without cycles is called a tree.
不带有环的图称为无环图Acyclic graph。不带有有向环的有向图称为有向无环图Directed acyclic graph。没有环的连接图称为树Tree。
*The '''length''' of a circuit or cycle is the number of edges involved.
*The '''length''' of a circuit or cycle is the number of edges involved.
* 回路是一条非空路径，其中第一个和最后一个顶点重复。设图''G =（V，E，ϕ）''，回路是具有顶点序列（''v1，v2，...，vn，v1''）的非空路径（''e1，e2，…，en''）。
* 回路Circuit是一条非空路径，其中第一个和最后一个顶点重复。设图''G =（V，E，ϕ）''，那么回路是具有顶点序列（''v1，v2，...，vn，v1''）的非空路径（''e1，e2，…，en''）。
* 在一个环或简单回路中，唯一重复的顶点是起始点和最终点。
* 在一个环或简单回路中，唯一重复的顶点是起始点和最终点。
* 一个回路或环的长度指的是相关连边的数量。
* 一个回路或环的长度指的是相关连边的数量。
== Chordless cycles 无弦环 ==
== Chordless cycles 无弦环 ==
[[File:Graph with Chordless and Chorded Cycles.svg|thumb|right|In this graph the green cycle (A-B-C-D-E-F-A) is chordless whereas the red cycle (G-H-I-J-K-L-G) is not. This is because the edge K-I is a chord.此图中的绿色环（A-B-C-D-E-F-A）是无弦的，而红色环（G-H-I-J-K-L-G）则是有弦的。因为连边K-I是弦。]]
[[文件:Graph with Chordless and Chorded Cycles.png|200px|thumb|left|此图中的绿色环（A-B-C-D-E-F-A）是无弦的，而红色环（G-H-I-J-K-L-G）则是有弦的。因为连边K-I是弦。]]