Cycle (graph theory)

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.

A graph without cycles is called an acyclic graph (or a forest). A directed graph without directed cycles is called a directed acyclic graph. A connected graph without cycles is called a tree.