def test_edmonds_undirected_graph(self) -> None:
g = Graph([("s", "t", 10), ("s", "y", 5), ("t", "y", 2)])
# Edmonds' algorithm does not work on undirected graphs.
with pytest.raises(exception.GraphTypeNotSupported):
for _ in directed.edmonds(g):
pass
def test_edmonds_unfeasible_spanning_arborescence(self) -> None:
"""Test to ensure that Unfeasible raised if a digraph does not contain a spanning
arborescence."""
g = DiGraph([("a", "b", 1), ("c", "d", 3)])
with pytest.raises(exception.Unfeasible):
_ = next(directed.edmonds(g, find_spanning_arborescence=True))
def test_edmonds_empty_graph(self) -> None:
g = DiGraph()
# Edmonds' algorithm does not work on empty graphs.
with pytest.raises(exception.Unfeasible):
for _ in directed.edmonds(g):
pass
def test_edmonds_min_arborescence_multigraph(self) -> None:
g = MultiDiGraph([
("a", "b", 1),
("a", "b", 2),
("b", "c", 3),
("b", "c", 6),
("c", "d", 5),
("c", "d", 10),
("d", "a", 2),
("d", "a", 4),
])
spanning_edges_min_arborescence = {("d", "a"), ("a", "b"), ("b", "c")}
arborescence = next(
directed.edmonds(g, minimum=True, find_spanning_arborescence=True))
for edge_label in spanning_edges_min_arborescence:
assert edge_label in arborescence
assert len(arborescence.edges()
) == 3, "min spanning arborescence should have 3 edges"
weight = 0.0
for edge in spanning_edges_min_arborescence:
weight += min(
c.weight
for c in arborescence.get_edge(edge[0], edge[1]).connections())
assert weight == 6
def test_edmonds_min_directed_forest(self) -> None:
g = DiGraph(test_edges_multi_tree)
main_arborescence = {("j", "g"), ("g", "h"), ("h", "i"), ("g", "c")}
count = 0
weight = 0.0
for arborescence in directed.edmonds(g,
minimum=True,
find_spanning_arborescence=False):
count += 1
weight += arborescence.weight
if len(arborescence) > 2:
for edge_label in main_arborescence:
assert edge_label in arborescence
assert count == 5, "min branching should have 5 arborescences"
assert weight == -24
def test_edmonds_max_directed_forest(self) -> None:
g = DiGraph(test_edges_multi_tree)
main_arborescence = {("d", "a"), ("a", "b"), ("b", "c"), ("c", "f")}
count = 0
weight = 0.0
for arborescence in directed.edmonds(g,
minimum=False,
find_spanning_arborescence=False):
count += 1
weight += arborescence.weight
if len(arborescence) > 1:
for edge_label in main_arborescence:
assert edge_label in arborescence
assert count == 6, "max branching should have 6 arborescences"
assert weight == 20
def test_edmonds_min_spanning_arborescence(self) -> None:
g = DiGraph(test_edges_acyclic)
spanning_edges_min_arborescence = {
("a", "e"),
("a", "b"),
("b", "c"),
("g", "h"),
("f", "g"),
("c", "f"),
("c", "d"),
}
arborescence = next(
directed.edmonds(g, minimum=True, find_spanning_arborescence=True))
for edge_label in spanning_edges_min_arborescence:
assert edge_label in arborescence
assert arborescence.weight == 30, "min spanning arborescence weight should be 30"
def test_edmonds_max_spanning_arborescence_cyclic_graph(self) -> None:
g = DiGraph(test_edges_cyclic)
spanning_edges_max_arborescence = {
("b", "a"),
("b", "c"),
("b", "g"),
("g", "h"),
("h", "d"),
("d", "e"),
("e", "f"),
}
arborescence = next(
directed.edmonds(g, minimum=False,
find_spanning_arborescence=True))
for edge_label in spanning_edges_max_arborescence:
assert edge_label in arborescence
assert arborescence.weight == 28, "max spanning arborescence weight should be 28"