cycle

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. A directed graph without directed cycles is called a directed acyclic graph. A connected graph without cycles is called a tree. Definitions Circuit and cycle A circuit is a non-empty trail in which the first and last vertices are equal (closed trail). Let be a graph. A circuit is a non-empty trail with a vertex sequence . A cycle or simple circuit is a circuit in which only the first and last vertices are equal. n is called the length of the circuit resp. length of the cycle.