ShortestPathSpanningTree[g, v] constructs a shortest-path spanning tree rooted at , so that a shortest path in graph from to any other vertex is a path in the tree.
To use ShortestPathSpanningTree, you first need to load the Combinatorica Package using Needs["Combinatorica`"].
An option Algorithm that takes on the values Automatic, Dijkstra, or BellmanFord is provided. This allows a choice between Dijkstra's algorithm and the Bellman-Ford algorithm.
The default is Algorithm->Automatic. In this case, depending on whether edges have negative weights and depending on the density of the graph, the algorithm chooses between BellmanFord and Dijkstra.