all simple paths

(classic problem)

Definition: Find all simple paths from a starting vertex (source) to a destination vertex (sink) in a directed graph. In an undirected graph, find all simple paths between two vertices.

See also all pairs shortest path.

Note: The paths may be enumerated with a depth-first search. The search can avoid repeating vertices by marking them as they are visited in the recursion, then removing the mark just before returning from the recursive call.

Author: PEB

Go to the Dictionary of Algorithms and Data Structures home page.

If you have suggestions, corrections, or comments, please get in touch with Paul Black.

Entry modified 2 September 2008.
HTML page formatted Tue Jan 16 10:34:44 2018.

Cite this as:
Paul E. Black, "all simple paths", in Dictionary of Algorithms and Data Structures [online], Vreda Pieterse and Paul E. Black, eds. 2 September 2008. (accessed TODAY) Available from: