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import pytest
import networkx as nx
from networkx.generators import line
from networkx.utils import edges_equal
class TestGeneratorLine:
def test_star(self):
G = nx.star_graph(5)
L = nx.line_graph(G)
assert nx.is_isomorphic(L, nx.complete_graph(5))
def test_path(self):
G = nx.path_graph(5)
L = nx.line_graph(G)
assert nx.is_isomorphic(L, nx.path_graph(4))
def test_cycle(self):
G = nx.cycle_graph(5)
L = nx.line_graph(G)
assert nx.is_isomorphic(L, G)
def test_digraph1(self):
G = nx.DiGraph([(0, 1), (0, 2), (0, 3)])
L = nx.line_graph(G)
# no edge graph, but with nodes
assert L.adj == {(0, 1): {}, (0, 2): {}, (0, 3): {}}
def test_multigraph1(self):
G = nx.MultiGraph([(0, 1), (0, 1), (1, 0), (0, 2), (2, 0), (0, 3)])
L = nx.line_graph(G)
# no edge graph, but with nodes
assert edges_equal(
L.edges(),
[
((0, 3, 0), (0, 1, 0)),
((0, 3, 0), (0, 2, 0)),
((0, 3, 0), (0, 2, 1)),
((0, 3, 0), (0, 1, 1)),
((0, 3, 0), (0, 1, 2)),
((0, 1, 0), (0, 1, 1)),
((0, 1, 0), (0, 2, 0)),
((0, 1, 0), (0, 1, 2)),
((0, 1, 0), (0, 2, 1)),
((0, 1, 1), (0, 1, 2)),
((0, 1, 1), (0, 2, 0)),
((0, 1, 1), (0, 2, 1)),
((0, 1, 2), (0, 2, 0)),
((0, 1, 2), (0, 2, 1)),
((0, 2, 0), (0, 2, 1)),
],
)
def test_multigraph2(self):
G = nx.MultiGraph([(1, 2), (2, 1)])
L = nx.line_graph(G)
assert edges_equal(L.edges(), [((1, 2, 0), (1, 2, 1))])
def test_multidigraph1(self):
G = nx.MultiDiGraph([(1, 2), (2, 1)])
L = nx.line_graph(G)
assert edges_equal(L.edges(), [((1, 2, 0), (2, 1, 0)), ((2, 1, 0), (1, 2, 0))])
def test_multidigraph2(self):
G = nx.MultiDiGraph([(0, 1), (0, 1), (0, 1), (1, 2)])
L = nx.line_graph(G)
assert edges_equal(
L.edges(),
[((0, 1, 0), (1, 2, 0)), ((0, 1, 1), (1, 2, 0)), ((0, 1, 2), (1, 2, 0))],
)
def test_digraph2(self):
G = nx.DiGraph([(0, 1), (1, 2), (2, 3)])
L = nx.line_graph(G)
assert edges_equal(L.edges(), [((0, 1), (1, 2)), ((1, 2), (2, 3))])
def test_create1(self):
G = nx.DiGraph([(0, 1), (1, 2), (2, 3)])
L = nx.line_graph(G, create_using=nx.Graph())
assert edges_equal(L.edges(), [((0, 1), (1, 2)), ((1, 2), (2, 3))])
def test_create2(self):
G = nx.Graph([(0, 1), (1, 2), (2, 3)])
L = nx.line_graph(G, create_using=nx.DiGraph())
assert edges_equal(L.edges(), [((0, 1), (1, 2)), ((1, 2), (2, 3))])
class TestGeneratorInverseLine:
def test_example(self):
G = nx.Graph()
G_edges = [
[1, 2],
[1, 3],
[1, 4],
[1, 5],
[2, 3],
[2, 5],
[2, 6],
[2, 7],
[3, 4],
[3, 5],
[6, 7],
[6, 8],
[7, 8],
]
G.add_edges_from(G_edges)
H = nx.inverse_line_graph(G)
solution = nx.Graph()
solution_edges = [
("a", "b"),
("a", "c"),
("a", "d"),
("a", "e"),
("c", "d"),
("e", "f"),
("e", "g"),
("f", "g"),
]
solution.add_edges_from(solution_edges)
assert nx.is_isomorphic(H, solution)
def test_example_2(self):
G = nx.Graph()
G_edges = [[1, 2], [1, 3], [2, 3], [3, 4], [3, 5], [4, 5]]
G.add_edges_from(G_edges)
H = nx.inverse_line_graph(G)
solution = nx.Graph()
solution_edges = [("a", "c"), ("b", "c"), ("c", "d"), ("d", "e"), ("d", "f")]
solution.add_edges_from(solution_edges)
assert nx.is_isomorphic(H, solution)
def test_pair(self):
G = nx.path_graph(2)
H = nx.inverse_line_graph(G)
solution = nx.path_graph(3)
assert nx.is_isomorphic(H, solution)
def test_line(self):
G = nx.path_graph(5)
solution = nx.path_graph(6)
H = nx.inverse_line_graph(G)
assert nx.is_isomorphic(H, solution)
def test_triangle_graph(self):
G = nx.complete_graph(3)
H = nx.inverse_line_graph(G)
alternative_solution = nx.Graph()
alternative_solution.add_edges_from([[0, 1], [0, 2], [0, 3]])
# there are two alternative inverse line graphs for this case
# so long as we get one of them the test should pass
assert nx.is_isomorphic(H, G) or nx.is_isomorphic(H, alternative_solution)
def test_cycle(self):
G = nx.cycle_graph(5)
H = nx.inverse_line_graph(G)
assert nx.is_isomorphic(H, G)
def test_empty(self):
G = nx.Graph()
H = nx.inverse_line_graph(G)
assert nx.is_isomorphic(H, nx.complete_graph(1))
def test_K1(self):
G = nx.complete_graph(1)
H = nx.inverse_line_graph(G)
solution = nx.path_graph(2)
assert nx.is_isomorphic(H, solution)
def test_edgeless_graph(self):
G = nx.empty_graph(5)
with pytest.raises(nx.NetworkXError, match="edgeless graph"):
nx.inverse_line_graph(G)
def test_selfloops_error(self):
G = nx.cycle_graph(4)
G.add_edge(0, 0)
pytest.raises(nx.NetworkXError, nx.inverse_line_graph, G)
def test_non_line_graphs(self):
# Tests several known non-line graphs for impossibility
# Adapted from L.W.Beineke, "Characterizations of derived graphs"
# claw graph
claw = nx.star_graph(3)
pytest.raises(nx.NetworkXError, nx.inverse_line_graph, claw)
# wheel graph with 6 nodes
wheel = nx.wheel_graph(6)
pytest.raises(nx.NetworkXError, nx.inverse_line_graph, wheel)
# K5 with one edge remove
K5m = nx.complete_graph(5)
K5m.remove_edge(0, 1)
pytest.raises(nx.NetworkXError, nx.inverse_line_graph, K5m)
# graph without any odd triangles (contains claw as induced subgraph)
G = nx.compose(nx.path_graph(2), nx.complete_bipartite_graph(2, 3))
pytest.raises(nx.NetworkXError, nx.inverse_line_graph, G)
## Variations on a diamond graph
# Diamond + 2 edges (+ "roof")
G = nx.diamond_graph()
G.add_edges_from([(4, 0), (5, 3)])
pytest.raises(nx.NetworkXError, nx.inverse_line_graph, G)
G.add_edge(4, 5)
pytest.raises(nx.NetworkXError, nx.inverse_line_graph, G)
# Diamond + 2 connected edges
G = nx.diamond_graph()
G.add_edges_from([(4, 0), (4, 3)])
pytest.raises(nx.NetworkXError, nx.inverse_line_graph, G)
# Diamond + K3 + one edge (+ 2*K3)
G = nx.diamond_graph()
G.add_edges_from([(4, 0), (4, 1), (4, 2), (5, 3)])
pytest.raises(nx.NetworkXError, nx.inverse_line_graph, G)
G.add_edges_from([(5, 1), (5, 2)])
pytest.raises(nx.NetworkXError, nx.inverse_line_graph, G)
# 4 triangles
G = nx.diamond_graph()
G.add_edges_from([(4, 0), (4, 1), (5, 2), (5, 3)])
pytest.raises(nx.NetworkXError, nx.inverse_line_graph, G)
def test_wrong_graph_type(self):
G = nx.DiGraph()
G_edges = [[0, 1], [0, 2], [0, 3]]
G.add_edges_from(G_edges)
pytest.raises(nx.NetworkXNotImplemented, nx.inverse_line_graph, G)
G = nx.MultiGraph()
G_edges = [[0, 1], [0, 2], [0, 3]]
G.add_edges_from(G_edges)
pytest.raises(nx.NetworkXNotImplemented, nx.inverse_line_graph, G)
def test_line_inverse_line_complete(self):
G = nx.complete_graph(10)
H = nx.line_graph(G)
J = nx.inverse_line_graph(H)
assert nx.is_isomorphic(G, J)
def test_line_inverse_line_path(self):
G = nx.path_graph(10)
H = nx.line_graph(G)
J = nx.inverse_line_graph(H)
assert nx.is_isomorphic(G, J)
def test_line_inverse_line_hypercube(self):
G = nx.hypercube_graph(5)
H = nx.line_graph(G)
J = nx.inverse_line_graph(H)
assert nx.is_isomorphic(G, J)
def test_line_inverse_line_cycle(self):
G = nx.cycle_graph(10)
H = nx.line_graph(G)
J = nx.inverse_line_graph(H)
assert nx.is_isomorphic(G, J)
def test_line_inverse_line_star(self):
G = nx.star_graph(20)
H = nx.line_graph(G)
J = nx.inverse_line_graph(H)
assert nx.is_isomorphic(G, J)
def test_line_inverse_line_multipartite(self):
G = nx.complete_multipartite_graph(3, 4, 5)
H = nx.line_graph(G)
J = nx.inverse_line_graph(H)
assert nx.is_isomorphic(G, J)
def test_line_inverse_line_dgm(self):
G = nx.dorogovtsev_goltsev_mendes_graph(4)
H = nx.line_graph(G)
J = nx.inverse_line_graph(H)
assert nx.is_isomorphic(G, J)
def test_line_different_node_types(self):
G = nx.path_graph([1, 2, 3, "a", "b", "c"])
H = nx.line_graph(G)
J = nx.inverse_line_graph(H)
assert nx.is_isomorphic(G, J)
class TestGeneratorPrivateFunctions:
def test_triangles_error(self):
G = nx.diamond_graph()
pytest.raises(nx.NetworkXError, line._triangles, G, (4, 0))
pytest.raises(nx.NetworkXError, line._triangles, G, (0, 3))
def test_odd_triangles_error(self):
G = nx.diamond_graph()
pytest.raises(nx.NetworkXError, line._odd_triangle, G, (0, 1, 4))
pytest.raises(nx.NetworkXError, line._odd_triangle, G, (0, 1, 3))
def test_select_starting_cell_error(self):
G = nx.diamond_graph()
pytest.raises(nx.NetworkXError, line._select_starting_cell, G, (4, 0))
pytest.raises(nx.NetworkXError, line._select_starting_cell, G, (0, 3))
def test_diamond_graph(self):
G = nx.diamond_graph()
for edge in G.edges:
cell = line._select_starting_cell(G, starting_edge=edge)
# Starting cell should always be one of the two triangles
assert len(cell) == 3
assert all(v in G[u] for u in cell for v in cell if u != v)
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