def min_tree(self):
a = WeightedGraph()
dsu = DSU()
edges = list()
for v in self.vertexes.keys():
dsu.make_set(v)
a.add_vertex(v)
for vertex in self.vertexes[v]:
edges.append((self.vertexes[v][vertex], (v, vertex)))
for (_, (u, v)) in sorted(edges):
if dsu.find_set(u) != dsu.find_set(v):
a.add_direct_link(u, v, self.vertexes[u][v])
dsu.union_sets(u, v)
return a
