Editing Cycle (graph theory) (section)

=== Algorithm ===
The aforementioned use of depth-first search to find a cycle can be described as follows:
 For every vertex v: visited(v) = finished(v) = false
 For every vertex v: DFS(v)
where
 DFS(v) =
   if finished(v): return
   if visited(v):
     "Cycle found"
     return
   visited(v) = true
   for every neighbour w: DFS(w)
   finished(v) = true

For undirected graphs, "neighbour" means all vertices connected to ''v'', except for the one that recursively called ''DFS(v)''. This omission prevents the algorithm from finding a trivial cycle of the form ''v''→''w''→''v''; these exist in every undirected graph with at least one edge.  

A variant using [[breadth-first search]] instead will find a cycle of the smallest possible length.