# Cycle (graph theory)

## Trail in which only the first and last vertices are equal. / From Wikipedia, the free encyclopedia

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In graph theory, a **cycle** in a graph is a non-empty trail in which only the first and last vertices are equal. A **directed cycle** in a directed graph is a non-empty directed trail in which only the first and last vertices are equal.

Trail in which only the first and last vertices are equal.

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*.

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