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FindShortestPath

 FindShortestPath finds the shortest path from source vertex s to target vertex t in the graph g. FindShortestPath[g, s, All]generates a ShortestPathFunction[...] which can be applied repeatedly to different t. FindShortestPath[g, All, t]generates a ShortestPathFunction[...] which can be applied repeatedly to different s. FindShortestPath[g, All, All]generates a ShortestPathFunction[...] which can be applied to different s and t.
• For an unweighted graph, edge length is assumed to be 1.
• For a weighted graph, edge length is taken to be the weight.
• A Method option can also be given. Possible Method settings include:
 "BellmanFord" supports positive and negative weights "Dijkstra" supports positive weights
Find a shortest path between two individual vertices in a graph:
Highlight the path:
Find a shortest path between two individual vertices in a graph:
 Out[1]=
 Out[2]=
Highlight the path:
 Out[3]=
 Scope   (6)
FindShortestPath works with undirected graphs:
Directed graphs:
Weighted graphs:
The shortest path has the smallest total edge weight:
Find the shortest paths from one vertex to all vertices:
Apply the ShortestPathFunction to every vertex of the graph:
Find the shortest paths to one vertex from all vertices:
Apply the ShortestPathFunction to every vertex of the graph:
Works with large graphs:
 Options   (3)
The method is automatically chosen depending on input:
method will use the weight 1 for every edge:
can be used for graphs with positive edge weights only:
 Applications   (3)
Find the shortest path in a tree:
Find the shortest path along the seams of a football:
Create a maze by random depth-first search of a grid graph:
Restore vertex coordinates:
Solve the maze:
The distance between two vertices can be found using the shortest path:
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