ShortestPath(G, u, v) returns a shortest path from u to v in G using a breadth-first search. The output is a list of vertices in the order they appear on the path. If no such a path exists, an error message is displayed.

If G is undirected, the output is a shortest path between u and v. If G is directed, the output is a shortest directed path from u to v.

Edge weights are ignored.

To compute shortest paths with respect to edge weights, use either DijkstrasAlgorithm or BellmanFordAlgorithm.

$\mathrm{with}\left(\mathrm{GraphTheory}\right)\:$

$\mathrm{C6}≔\mathrm{CycleGraph}\left(6\right)$

$\mathrm{C6}≔\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 6\; vertices\; and\; 6\; edge(s)}$

$\mathrm{IsReachable}\left(\mathrm{C6}\,1\,5\right)$

$\mathrm{true}$

$\mathrm{ShortestPath}\left(\mathrm{C6}\,1\,5\right)$

$\left[1\,6\,5\right]$