Editing Depth-first search (section)

==Example==
[[File:Depth-First-Search.gif|thumb|Animated example of a depth-first search]]
For the following graph:

[[File:graph.traversal.example.svg|200px|alt=An undirected graph with edges AB, BD, BF, FE, AC, CG, AE]]

A depth-first search starting at the node A, assuming that the left edges in the shown graph are chosen before right edges, and assuming the search remembers previously visited nodes and will not repeat them (since this is a small graph), will visit the nodes in the following order: A, B, D, F, E, C, G.  The edges traversed in this search form a [[Trémaux tree]], a structure with important applications in [[graph theory]].
Performing the same search without remembering previously visited nodes results in visiting the nodes in the order A, B, D, F, E, A, B, D, F, E, etc. forever, caught in the A, B, D, F, E cycle and never reaching C or G.

[[Iterative deepening depth-first search|Iterative deepening]] is one technique to avoid this infinite loop and would reach all nodes.