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import pytest
import networkx as nx
from networkx.algorithms.approximation.steinertree import (
_remove_nonterminal_leaves,
metric_closure,
steiner_tree,
)
from networkx.utils import edges_equal
class TestSteinerTree:
@classmethod
def setup_class(cls):
G1 = nx.Graph()
G1.add_edge(1, 2, weight=10)
G1.add_edge(2, 3, weight=10)
G1.add_edge(3, 4, weight=10)
G1.add_edge(4, 5, weight=10)
G1.add_edge(5, 6, weight=10)
G1.add_edge(2, 7, weight=1)
G1.add_edge(7, 5, weight=1)
G2 = nx.Graph()
G2.add_edge(0, 5, weight=6)
G2.add_edge(1, 2, weight=2)
G2.add_edge(1, 5, weight=3)
G2.add_edge(2, 4, weight=4)
G2.add_edge(3, 5, weight=5)
G2.add_edge(4, 5, weight=1)
G3 = nx.Graph()
G3.add_edge(1, 2, weight=8)
G3.add_edge(1, 9, weight=3)
G3.add_edge(1, 8, weight=6)
G3.add_edge(1, 10, weight=2)
G3.add_edge(1, 14, weight=3)
G3.add_edge(2, 3, weight=6)
G3.add_edge(3, 4, weight=3)
G3.add_edge(3, 10, weight=2)
G3.add_edge(3, 11, weight=1)
G3.add_edge(4, 5, weight=1)
G3.add_edge(4, 11, weight=1)
G3.add_edge(5, 6, weight=4)
G3.add_edge(5, 11, weight=2)
G3.add_edge(5, 12, weight=1)
G3.add_edge(5, 13, weight=3)
G3.add_edge(6, 7, weight=2)
G3.add_edge(6, 12, weight=3)
G3.add_edge(6, 13, weight=1)
G3.add_edge(7, 8, weight=3)
G3.add_edge(7, 9, weight=3)
G3.add_edge(7, 11, weight=5)
G3.add_edge(7, 13, weight=2)
G3.add_edge(7, 14, weight=4)
G3.add_edge(8, 9, weight=2)
G3.add_edge(9, 14, weight=1)
G3.add_edge(10, 11, weight=2)
G3.add_edge(10, 14, weight=1)
G3.add_edge(11, 12, weight=1)
G3.add_edge(11, 14, weight=7)
G3.add_edge(12, 14, weight=3)
G3.add_edge(12, 15, weight=1)
G3.add_edge(13, 14, weight=4)
G3.add_edge(13, 15, weight=1)
G3.add_edge(14, 15, weight=2)
cls.G1 = G1
cls.G2 = G2
cls.G3 = G3
cls.G1_term_nodes = [1, 2, 3, 4, 5]
cls.G2_term_nodes = [0, 2, 3]
cls.G3_term_nodes = [1, 3, 5, 6, 8, 10, 11, 12, 13]
cls.methods = ["kou", "mehlhorn"]
def test_connected_metric_closure(self):
G = self.G1.copy()
G.add_node(100)
pytest.raises(nx.NetworkXError, metric_closure, G)
def test_metric_closure(self):
M = metric_closure(self.G1)
mc = [
(1, 2, {"distance": 10, "path": [1, 2]}),
(1, 3, {"distance": 20, "path": [1, 2, 3]}),
(1, 4, {"distance": 22, "path": [1, 2, 7, 5, 4]}),
(1, 5, {"distance": 12, "path": [1, 2, 7, 5]}),
(1, 6, {"distance": 22, "path": [1, 2, 7, 5, 6]}),
(1, 7, {"distance": 11, "path": [1, 2, 7]}),
(2, 3, {"distance": 10, "path": [2, 3]}),
(2, 4, {"distance": 12, "path": [2, 7, 5, 4]}),
(2, 5, {"distance": 2, "path": [2, 7, 5]}),
(2, 6, {"distance": 12, "path": [2, 7, 5, 6]}),
(2, 7, {"distance": 1, "path": [2, 7]}),
(3, 4, {"distance": 10, "path": [3, 4]}),
(3, 5, {"distance": 12, "path": [3, 2, 7, 5]}),
(3, 6, {"distance": 22, "path": [3, 2, 7, 5, 6]}),
(3, 7, {"distance": 11, "path": [3, 2, 7]}),
(4, 5, {"distance": 10, "path": [4, 5]}),
(4, 6, {"distance": 20, "path": [4, 5, 6]}),
(4, 7, {"distance": 11, "path": [4, 5, 7]}),
(5, 6, {"distance": 10, "path": [5, 6]}),
(5, 7, {"distance": 1, "path": [5, 7]}),
(6, 7, {"distance": 11, "path": [6, 5, 7]}),
]
assert edges_equal(list(M.edges(data=True)), mc)
def test_steiner_tree(self):
valid_steiner_trees = [
[
[
(1, 2, {"weight": 10}),
(2, 3, {"weight": 10}),
(2, 7, {"weight": 1}),
(3, 4, {"weight": 10}),
(5, 7, {"weight": 1}),
],
[
(1, 2, {"weight": 10}),
(2, 7, {"weight": 1}),
(3, 4, {"weight": 10}),
(4, 5, {"weight": 10}),
(5, 7, {"weight": 1}),
],
[
(1, 2, {"weight": 10}),
(2, 3, {"weight": 10}),
(2, 7, {"weight": 1}),
(4, 5, {"weight": 10}),
(5, 7, {"weight": 1}),
],
],
[
[
(0, 5, {"weight": 6}),
(1, 2, {"weight": 2}),
(1, 5, {"weight": 3}),
(3, 5, {"weight": 5}),
],
[
(0, 5, {"weight": 6}),
(4, 2, {"weight": 4}),
(4, 5, {"weight": 1}),
(3, 5, {"weight": 5}),
],
],
[
[
(1, 10, {"weight": 2}),
(3, 10, {"weight": 2}),
(3, 11, {"weight": 1}),
(5, 12, {"weight": 1}),
(6, 13, {"weight": 1}),
(8, 9, {"weight": 2}),
(9, 14, {"weight": 1}),
(10, 14, {"weight": 1}),
(11, 12, {"weight": 1}),
(12, 15, {"weight": 1}),
(13, 15, {"weight": 1}),
]
],
]
for method in self.methods:
for G, term_nodes, valid_trees in zip(
[self.G1, self.G2, self.G3],
[self.G1_term_nodes, self.G2_term_nodes, self.G3_term_nodes],
valid_steiner_trees,
):
S = steiner_tree(G, term_nodes, method=method)
assert any(
edges_equal(list(S.edges(data=True)), valid_tree)
for valid_tree in valid_trees
)
def test_multigraph_steiner_tree(self):
G = nx.MultiGraph()
G.add_edges_from(
[
(1, 2, 0, {"weight": 1}),
(2, 3, 0, {"weight": 999}),
(2, 3, 1, {"weight": 1}),
(3, 4, 0, {"weight": 1}),
(3, 5, 0, {"weight": 1}),
]
)
terminal_nodes = [2, 4, 5]
expected_edges = [
(2, 3, 1, {"weight": 1}), # edge with key 1 has lower weight
(3, 4, 0, {"weight": 1}),
(3, 5, 0, {"weight": 1}),
]
for method in self.methods:
S = steiner_tree(G, terminal_nodes, method=method)
assert edges_equal(S.edges(data=True, keys=True), expected_edges)
def test_remove_nonterminal_leaves(self):
G = nx.path_graph(10)
_remove_nonterminal_leaves(G, [4, 5, 6])
assert list(G) == [4, 5, 6] # only the terminal nodes are left
@pytest.mark.parametrize("method", ("kou", "mehlhorn"))
def test_steiner_tree_weight_attribute(method):
G = nx.star_graph(4)
# Add an edge attribute that is named something other than "weight"
nx.set_edge_attributes(G, {e: 10 for e in G.edges}, name="distance")
H = nx.approximation.steiner_tree(G, [1, 3], method=method, weight="distance")
assert nx.utils.edges_equal(H.edges, [(0, 1), (0, 3)])
@pytest.mark.parametrize("method", ("kou", "mehlhorn"))
def test_steiner_tree_multigraph_weight_attribute(method):
G = nx.cycle_graph(3, create_using=nx.MultiGraph)
nx.set_edge_attributes(G, {e: 10 for e in G.edges}, name="distance")
G.add_edge(2, 0, distance=5)
H = nx.approximation.steiner_tree(G, list(G), method=method, weight="distance")
assert len(H.edges) == 2 and H.has_edge(2, 0, key=1)
assert sum(dist for *_, dist in H.edges(data="distance")) == 15
@pytest.mark.parametrize("method", (None, "mehlhorn", "kou"))
def test_steiner_tree_methods(method):
G = nx.star_graph(4)
expected = nx.Graph([(0, 1), (0, 3)])
st = nx.approximation.steiner_tree(G, [1, 3], method=method)
assert nx.utils.edges_equal(st.edges, expected.edges)
def test_steiner_tree_method_invalid():
G = nx.star_graph(4)
with pytest.raises(
ValueError, match="invalid_method is not a valid choice for an algorithm."
):
nx.approximation.steiner_tree(G, terminal_nodes=[1, 3], method="invalid_method")
def test_steiner_tree_remove_non_terminal_leaves_self_loop_edges():
# To verify that the last step of the steiner tree approximation
# behaves in the case where a non-terminal leaf has a self loop edge
G = nx.path_graph(10)
# Add self loops to the terminal nodes
G.add_edges_from([(2, 2), (3, 3), (4, 4), (7, 7), (8, 8)])
# Remove non-terminal leaves
_remove_nonterminal_leaves(G, [4, 5, 6, 7])
# The terminal nodes should be left
assert list(G) == [4, 5, 6, 7] # only the terminal nodes are left
def test_steiner_tree_non_terminal_leaves_multigraph_self_loop_edges():
# To verify that the last step of the steiner tree approximation
# behaves in the case where a non-terminal leaf has a self loop edge
G = nx.MultiGraph()
G.add_edges_from([(i, i + 1) for i in range(10)])
G.add_edges_from([(2, 2), (3, 3), (4, 4), (4, 4), (7, 7)])
# Remove non-terminal leaves
_remove_nonterminal_leaves(G, [4, 5, 6, 7])
# Only the terminal nodes should be left
assert list(G) == [4, 5, 6, 7]
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