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[{v->w,…},…] uses rules v->w to specify the graph g. 

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