ShortestPathSpanningTree

As of Version 10, most of the functionality of the Combinatorica package is built into the Wolfram System. »

ShortestPathSpanningTree[g,v]

constructs a shortest-path spanning tree rooted at v, so that a shortest path in graph g from v to any other vertex is a path in the tree.

Details and Options

ShortestPathSpanningTree functionality is now available in the built-in Wolfram Language function FindSpanningTree.
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.

Wolfram Language code: Needs["Combinatorica`"]

Wolfram Language code: g = FromAdjacencyMatrix[{{0, 1, 1, 1}, {1, 0, 1, 0}, {1, 1, 0, 1}, {1, 0, 1, 0}}];

Wolfram Language code: ShowGraph[g]

Wolfram Language code: ShortestPathSpanningTree[g, 1];

Wolfram Language code: ShowGraph[%]

ShortestPathSpanningTree has been superseded by FindSpanningTree:

Wolfram Language code: g = AdjacencyGraph[{{0, 1, 1, 1}, {1, 0, 1, 0}, {1, 1, 0, 1}, {1, 0, 1, 0}}]

Wolfram Language code: FindSpanningTree[g, 1]

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