
minimum_spanning_tree(+Graph, +DistanceArg, -Tree, -TreeWeight)

   Computes a minimum spanning tree and its weight

Arguments
   Graph               a graph structure
   DistanceArg         which argument of EdgeData to use as distance: integer
   Tree                a list of e/3 edge structures
   TreeWeight          sum of the tree's edge weights: number

Type
   library(graph_algorithms)

Description

    Computes a minimum spanning tree for the given graph. A minimum
    spanning tree is a smallest subset of the graph's edges that still
    connects all the graph's nodes. Such a tree is not unique and of
    course exists only if the original graph is itself connected.
    However, all minimum spanning trees will have the same cost.

    The computed tree is returned in Tree, which is simply a list of
    the edges that form the tree. The TreeWeight is the total length
    of the tree's edges, according to DistanceArg.

    DistanceArg refers to the graph's EdgeData information that was
    specified when the graph was constructed. If EdgeData is a simple
    number, then DistanceArg should be 0 and EdgeData will be taken
    as the length of the edge. If EdgeData is a compound data structure,
    DistanceArg should be a number between 1 and the arity of that
    structure and determines which argument of the EdgeData structure
    will be interpreted as the edge's length. Important: the distance
    information in EdgeData must be a non-negative number, and the
    numeric type (integer, float, etc) must be the same in all edges.

    If DistanceArg is given as -1, then any EdgeData is ignored and
    the length of every edge is assumed to be equal to 1.

    The direction of the graph's edges is ignored by this predicate.

    The implementation uses Kruskal's algorithm which has a complexity
    of O(Nedges*log(Nedges)).
    

Modes and Determinism
   minimum_spanning_tree(+, +, -, -) is semidet

Fail Conditions
   No spanning tree exists, i.e. the graph is not connected.

Examples
   
    ?- sample_graph(G), minimum_spanning_tree(G, 0, T, W).
    T = [e(2, 10, 1), e(4, 8, 1), e(9, 2, 1), e(7, 3, 2), ...]
    W = 16
    

See Also
   minimum_spanning_forest / 5
