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此词条由Jie翻译。

此词条由Jie翻译。

[[File:Graph cycle.svg|thumb| A graph with edges colored to illustrate path H-A-B (green), closed path or walk with a repeated vertex B-D-E-F-D-C-B (blue) and a cycle with no repeated edge or vertex H-D-G-H (red). 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|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）。]]

 

 

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.