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FindShortestPath[g,s,t]

finds the shortest path from source vertex s to target vertex t in the graph g.

FindShortestPath[g,s,All]

generates a ShortestPathFunction[…] that can be applied repeatedly to different t.

FindShortestPath[g,All,t]

generates a ShortestPathFunction[…] that can be applied repeatedly to different s.

FindShortestPath[g,All,All]

generates a ShortestPathFunction[…] that can be applied to different s and t.

FindShortestPath[{vw,…},…]

uses rules vw to specify the graph g.

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Specification  
Collection  
Options  
Method  
Applications  
Properties & Relations  
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FindShortestPath

FindShortestPath[g,s,t]

finds the shortest path from source vertex s to target vertex t in the graph g.

FindShortestPath[g,s,All]

generates a ShortestPathFunction[…] that can be applied repeatedly to different t.

FindShortestPath[g,All,t]

generates a ShortestPathFunction[…] that can be applied repeatedly to different s.

FindShortestPath[g,All,All]

generates a ShortestPathFunction[…] that can be applied to different s and t.

FindShortestPath[{vw,…},…]

uses rules vw to specify the graph g.

Details and Options

Examples

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Basic Examples  (1)

Find a shortest path between two individual vertices in a graph:

Wolfram Language code: g = [image];
Wolfram Language code: FindShortestPath[g, 3, 5]

Highlight the path:

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

Scope  (9)

Specification  (7)

FindShortestPath works with undirected graphs:

Wolfram Language code: GridGraph[{3, 4}, VertexSize -> {2 -> Medium, 7 -> Medium}]
Wolfram Language code: HighlightGraph[%, PathGraph@FindShortestPath[%, 2, 7]]

Directed graphs:

Wolfram Language code: g = [image];
Wolfram Language code: HighlightGraph[g, PathGraph[FindShortestPath[g, 1, 4], DirectedEdges -> True]]

Multigraphs:

Wolfram Language code: g = [image];
Wolfram Language code: HighlightGraph[g, PathGraph[FindShortestPath[g, 1, 4]]]

Mixed graphs:

Wolfram Language code: g = [image];
Wolfram Language code: HighlightGraph[g, Subgraph[g, FindShortestPath[g, 1, 4]]]

Weighted graphs:

Wolfram Language code: WeightedAdjacencyGraph[(| | | | | | --- | --- | ---- | ---- | | ∞ | 1.6 | 2 | 1.4 | | 1.6 | ∞ | 1.9 | ∞ | | 2 | 1.9 | ∞ | 0.62 | | 1.4 | ∞ | 0.62 | ∞ |), VertexSize -> {2 -> Small, 4 -> Small}]

The shortest path has the smallest total edge weight:

Wolfram Language code: HighlightGraph[%, PathGraph@FindShortestPath[%, 2, 4]]

Use rules to specify the graph:

Wolfram Language code: g = {12, 23, 31, 34, 45, 35};
Wolfram Language code: HighlightGraph[g, PathGraph[FindShortestPath[g, 1, 4], DirectedEdges -> True]]

Works with large graphs:

Wolfram Language code: g = GridGraph[{10, 10, 10, 10}];
Wolfram Language code: Timing[FindShortestPath[g, 1, 100]//Length]
Wolfram Language code: VertexCount[g]

Collection  (2)

Find the shortest paths from one vertex to all vertices:

Wolfram Language code: g = GridGraph[{2, 3}, DirectedEdges -> True, EdgeStyle -> Arrowheads[Small], VertexSize -> {1 -> Small}]
Wolfram Language code: spf = FindShortestPath[%, 1, All]

Apply the ShortestPathFunction to every vertex of the graph:

Wolfram Language code: Table[spf[v], {v, VertexList[g]}]
Wolfram Language code: HighlightGraph[g, PathGraph[#, DirectedEdges -> True]]& /@ %

Find the shortest paths to one vertex from all vertices:

Wolfram Language code: g = GridGraph[{2, 3}, DirectedEdges -> True, EdgeStyle -> Arrowheads[Small], VertexSize -> {6 -> Small}]
Wolfram Language code: spf = FindShortestPath[%, All, 6]

Apply the ShortestPathFunction to every vertex of the graph:

Wolfram Language code: Table[spf[v], {v, VertexList[g]}]
Wolfram Language code: HighlightGraph[g, PathGraph[#, DirectedEdges -> True]]& /@ %

Options  (3)

Method  (3)

The method is automatically chosen depending on input:

Wolfram Language code: {PetersenGraph[4, 1, VertexSize -> {1 -> Medium, 7 -> Medium}], PetersenGraph[4, 1, EdgeWeight -> {4, 0, 3, 1, 3, 2, 7, 8, 5, 2, 1, 6}, VertexSize -> {1 -> Medium, 7 -> Medium}]}
Wolfram Language code: Table[HighlightGraph[g, PathGraph@FindShortestPath[g, 1, 7]], {g, %}]

"UnitWeight" method will use the weight 1 for every edge:

Wolfram Language code: GridGraph[{2, 3}, EdgeWeight -> {5, 2, 2, 5, 1, 2, 2}, VertexSize -> {1 -> Small, 5 -> Small}]
Wolfram Language code: HighlightGraph[%, PathGraph@FindShortestPath[%, 1, 5, Method -> "UnitWeight"]]

"Dijkstra" can be used for graphs with positive edge weights only:

Wolfram Language code: GridGraph[{2, 3}, EdgeWeight -> {5, 2, 2, 5, 1, 2, 2}, VertexSize -> {1 -> Small, 5 -> Small}]
Wolfram Language code: HighlightGraph[%, PathGraph@FindShortestPath[%, 1, 5, Method -> "Dijkstra"]]

Applications  (3)

Find the shortest path in a tree:

Wolfram Language code: CompleteKaryTree[6, 2]
Wolfram Language code: HighlightGraph[%, PathGraph@FindShortestPath[%, 12, 57]]

Find the shortest path along the seams of a soccer ball:

Wolfram Language code: coords = PolyhedronData["SoccerBall", "Vertices"]; {Graphics3D[Join[{Glow[Gray], PolyhedronData["SoccerBall", "GraphicsComplex"], Red}, Sphere[#, 0.3]& /@ coords[[{19, 30}]]]], g = PolyhedronData["SoccerBall", "Skeleton"]}
Wolfram Language code: path = PathGraph@FindShortestPath[g, 19, 30]; {HighlightGraph[g, path], Graphics3D[Join[{Glow[Gray], PolyhedronData["SoccerBall", "GraphicsComplex"], Red}, Sphere[#, 0.3]& /@ coords[[{19, 30}]], {Thick, Red, Line[coords[[VertexList[path]]]]}]]}

Create a maze by random depth-first search of a grid graph:

Wolfram Language code: g = GridGraph[{20, 30}]
Wolfram Language code: m = Graph[VertexList[g], Module[{stack = {RandomChoice[VertexList[g]]}}, Do[AnnotationValue[{g, v}, "Visited"] = False, {v, VertexList[g]}]; AnnotationValue[{g, First@stack}, "Visited"] = True; While[Not[stack == {}], With[{v = First@stack}, With[{adj = Cases[EdgeList[g, v_] /. {vu_ :> u, u_v :> u}, x_ /; ¬AnnotationValue[{g, x}, "Visited"]]}, If[adj == {}, stack = Rest@stack, With[{w = RandomChoice[adj]}, PrependTo[stack, w]; AnnotationValue[{g, w}, "Visited"] = True; Sow[vw]]]]]]]//Reap//Last//First, VertexCoordinates -> GraphEmbedding[g]];

Solve the maze:

Wolfram Language code: HighlightGraph[m, PathGraph@FindShortestPath[m, First@VertexList[m], Last@VertexList[m]]]

Properties & Relations  (1)

The distance between two vertices can be found using the shortest path:

Wolfram Language code: g = GridGraph[{3, 4}]
Wolfram Language code: FindShortestPath[%, 1, 12]
Wolfram Language code: Length[%] - 1
Wolfram Language code: GraphDistance[g, 1, 12]
Wolfram Research (2010), FindShortestPath, Wolfram Language function, https://reference.wolfram.com/language/ref/FindShortestPath.html (updated 2015).

Text

Wolfram Research (2010), FindShortestPath, Wolfram Language function, https://reference.wolfram.com/language/ref/FindShortestPath.html (updated 2015).

CMS

Wolfram Language. 2010. "FindShortestPath." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/FindShortestPath.html.

APA

Wolfram Language. (2010). FindShortestPath. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/FindShortestPath.html

BibTeX

@misc{reference.wolfram_2026_findshortestpath, author="Wolfram Research", title="{FindShortestPath}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/FindShortestPath.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_findshortestpath, organization={Wolfram Research}, title={FindShortestPath}, year={2015}, url={https://reference.wolfram.com/language/ref/FindShortestPath.html}, note=[Accessed: 12-June-2026]}