BUILT-IN MATHEMATICA SYMBOL

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.

	"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]=

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:

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:

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: