WOLFRAM

Wolfram Language & System Documentation Center

FindPath[g,s,t]

finds a path between vertex s and vertex t in the graph g.

FindPath[g,s,t,k]

finds a path of length at most k between vertex s and vertex t in the graph g.

FindPath[g,s,t,{k}]

finds a path of length exactly k.

FindPath[g,s,t,{kmin,kmax}]

finds a path of length between kmin and kmax.

FindPath[g,s,t,kspec,n]

finds at most n paths.

FindPath[{vw,…},…]

uses rules vw to specify the graph g.

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Specification  
Enumeration  
Applications  
Properties & Relations  
See Also
Related Guides
History
Cite this Page

FindPath

FindPath[g,s,t]

finds a path between vertex s and vertex t in the graph g.

FindPath[g,s,t,k]

finds a path of length at most k between vertex s and vertex t in the graph g.

FindPath[g,s,t,{k}]

finds a path of length exactly k.

FindPath[g,s,t,{kmin,kmax}]

finds a path of length between kmin and kmax.

FindPath[g,s,t,kspec,n]

finds at most n paths.

FindPath[{vw,…},…]

uses rules vw to specify the graph g.

Details

  • FindPath returns a list of paths from s to t. Each path is given as a list of vertices.
  • FindPath[g,s,t,kspec,All] finds all the paths.
  • For weighted graphs, FindPath[g,s,t,k] gives all paths with total weights at most k.
  • FindPath works with undirected graphs, directed graphs, weighted graphs, multigraphs, and mixed graphs.

Examples

open all close all

Basic Examples  (2)

Find a path between two individual vertices in a graph:

Wolfram Language code: g = [image];
Wolfram Language code: FindPath[g, 3, 2]

Highlight the path:

Wolfram Language code: HighlightGraph[g, PathGraph[First[%]]]

Find all paths between two individual vertices in a graph:

Wolfram Language code: g = ExampleData[{"NetworkGraph", "Friendship"}];
Wolfram Language code: FindPath[g, "Anna", "Larry", Infinity, All]

Scope  (12)

Specification  (7)

FindPath works with undirected graphs:

Wolfram Language code: FindPath[[image], 2, 7]

Directed graphs:

Wolfram Language code: FindPath[[image], 2, 12]

Multigraphs:

Wolfram Language code: FindPath[[image], 2, 7]

Mixed graphs:

Wolfram Language code: FindPath[[image], 2, 7]

Weighted graphs:

Wolfram Language code: FindPath[[image], 2, 4]

Use rules to specify the graph:

Wolfram Language code: FindPath[{1 -> 2, 1 -> 4, 2 -> 3, 2 -> 5, 3 -> 6, 4 -> 5, 4 -> 7, 5 -> 6, 5 -> 8, 6 -> 9, 7 -> 8, 7 -> 10, 8 -> 9, 8 -> 11, 9 -> 12, 10 -> 11, 11 -> 12}, 2, 12]

FindPath works with large graphs:

Wolfram Language code: g = GridGraph[{10, 10, 10, 10}];
Wolfram Language code: FindPath[g, 1, 10000]//Short//Timing

Enumeration  (5)

A path of length exactly 7:

Wolfram Language code: FindPath[[image], 1, 12, {7}]

A path of length at most 6:

Wolfram Language code: FindPath[[image], 1, 12, 6]

A path of length between 5 and 7:

Wolfram Language code: FindPath[[image], 1, 12, {5, 7}]

Find all paths between two individual vertices:

Wolfram Language code: FindPath[[image], 1, 12, Infinity, All]//Short

FindPath gives an empty list if there is no path:

Wolfram Language code: FindPath[[image], 1, 12]

Applications  (2)

Find paths of length at most 5 along the seams of a soccer ball:

Wolfram Language code: g = PolyhedronData["SoccerBall", "Skeleton"];
Wolfram Language code: path = FindPath[g, 19, 30, 6, All]

Highlight the paths:

Wolfram Language code: coords = PolyhedronData["SoccerBall", "Vertices"];
Wolfram Language code: Graphics3D[Join[{Glow[Gray], PolyhedronData["SoccerBall", "GraphicsComplex"], Red}, Sphere[#, 0.3]& /@ coords[[{19, 30}]], {Red, Tube[coords[[#]], 0.2]}]]& /@ path

Plan a trip in the London Underground:

Wolfram Language code: g = \!\(\*GraphicsBox[«4»]\);

Find a trip from Arsenal to Alperton with at most 16 stops:

Wolfram Language code: FindPath[g, "Arsenal", "Alperton", 17, All]

Properties & Relations  (2)

Find all shortest paths:

Wolfram Language code: s = 1; t = 12; g = GridGraph[{3, 4}, VertexSize -> {s -> Medium, t -> Medium}]
Wolfram Language code: FindPath[g, s, t, {GraphDistance[g, s, t]}, All]

Highlight results:

Wolfram Language code: HighlightGraph[g, PathGraph[#]]& /@ %

FindPath only returns simple paths:

Wolfram Language code: FindPath[[image], 1, 3, Infinity, All]
Wolfram Research (2014), FindPath, Wolfram Language function, https://reference.wolfram.com/language/ref/FindPath.html (updated 2015).

Text

Wolfram Research (2014), FindPath, Wolfram Language function, https://reference.wolfram.com/language/ref/FindPath.html (updated 2015).

CMS

Wolfram Language. 2014. "FindPath." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/FindPath.html.

APA

Wolfram Language. (2014). FindPath. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FindPath.html

BibTeX

@misc{reference.wolfram_2026_findpath, author="Wolfram Research", title="{FindPath}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/FindPath.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_findpath, organization={Wolfram Research}, title={FindPath}, year={2015}, url={https://reference.wolfram.com/language/ref/FindPath.html}, note=[Accessed: 13-June-2026]}