"Source: Text/Incidence/MultiGraph.text";
"Line: 3825";
"Date: Fri Sep 26 12:10:10 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Incidence/MultiGraph.text, line: 3825
// Example: H163E13 ()
print "Example: H163E13";
ei := GetEchoInput();
SetEchoInput(true);
G := MultiGraph< 5 | {1, 2}, {1, 2}, {1, 3}, {2, 4}, {3, 5}, {3, 4}, {4, 5} >;
E := EdgeSet(G);
AssignWeight(~G, E.1, 1);
AssignWeight(~G, E.3, 5);
AssignWeight(~G, E.5, 10);
AssignWeight(~G, E.7, 1);
AssignWeight(~G, E.9, -5);
AssignWeight(~G, E.11, 1);
AssignWeight(~G, E.13, 2);

V := VertexSet(G);
E := EdgeSet(G);
for e in E do
    e, "  ", Weight(e);
end for;
T := MinimumWeightTree(V!1);
ET := EdgeSet(T);
for e in ET do
    e, "  ", Weight(e);
end for;
DFST := DFSTree(V!1);
EDT := EdgeSet(DFST);
for e in EDT do
    u := InitialVertex(e);
    v := TerminalVertex(e);
    w := Min([ Weight(edge) : edge in Edges(V!u, V!v) ]);
    e, "  ", w;
end for;
SetEchoInput(ei);
