Graph cycle

A cycle on a graph is a path that starts and ends at the same vertex, with at least one edge and no other repeated vertices. In other words, a cycle is a closed loop in the graph.

• The length of a cycle is the number of edges it contains.

In short, a cycle is a closed loop that doesn’t visit any vertex twice (except the one it starts/ends at).

Visiting vertices and edges

• Only the starting vertex is visited twice.
• All other vertices and edges are visited exactly once.

Closed trail

A closed trail is like a cycle, but it allows vertices to be revisited, as long as no edges are repeated.

By definition, all cycles are closed trails, but not all closed trails are cycles.