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import collections
import pytest
import networkx as nx
class TestIsEulerian:
def test_is_eulerian(self):
assert nx.is_eulerian(nx.complete_graph(5))
assert nx.is_eulerian(nx.complete_graph(7))
assert nx.is_eulerian(nx.hypercube_graph(4))
assert nx.is_eulerian(nx.hypercube_graph(6))
assert not nx.is_eulerian(nx.complete_graph(4))
assert not nx.is_eulerian(nx.complete_graph(6))
assert not nx.is_eulerian(nx.hypercube_graph(3))
assert not nx.is_eulerian(nx.hypercube_graph(5))
assert not nx.is_eulerian(nx.petersen_graph())
assert not nx.is_eulerian(nx.path_graph(4))
def test_is_eulerian2(self):
# not connected
G = nx.Graph()
G.add_nodes_from([1, 2, 3])
assert not nx.is_eulerian(G)
# not strongly connected
G = nx.DiGraph()
G.add_nodes_from([1, 2, 3])
assert not nx.is_eulerian(G)
G = nx.MultiDiGraph()
G.add_edge(1, 2)
G.add_edge(2, 3)
G.add_edge(2, 3)
G.add_edge(3, 1)
assert not nx.is_eulerian(G)
class TestEulerianCircuit:
def test_eulerian_circuit_cycle(self):
G = nx.cycle_graph(4)
edges = list(nx.eulerian_circuit(G, source=0))
nodes = [u for u, v in edges]
assert nodes == [0, 3, 2, 1]
assert edges == [(0, 3), (3, 2), (2, 1), (1, 0)]
edges = list(nx.eulerian_circuit(G, source=1))
nodes = [u for u, v in edges]
assert nodes == [1, 2, 3, 0]
assert edges == [(1, 2), (2, 3), (3, 0), (0, 1)]
G = nx.complete_graph(3)
edges = list(nx.eulerian_circuit(G, source=0))
nodes = [u for u, v in edges]
assert nodes == [0, 2, 1]
assert edges == [(0, 2), (2, 1), (1, 0)]
edges = list(nx.eulerian_circuit(G, source=1))
nodes = [u for u, v in edges]
assert nodes == [1, 2, 0]
assert edges == [(1, 2), (2, 0), (0, 1)]
def test_eulerian_circuit_digraph(self):
G = nx.DiGraph()
nx.add_cycle(G, [0, 1, 2, 3])
edges = list(nx.eulerian_circuit(G, source=0))
nodes = [u for u, v in edges]
assert nodes == [0, 1, 2, 3]
assert edges == [(0, 1), (1, 2), (2, 3), (3, 0)]
edges = list(nx.eulerian_circuit(G, source=1))
nodes = [u for u, v in edges]
assert nodes == [1, 2, 3, 0]
assert edges == [(1, 2), (2, 3), (3, 0), (0, 1)]
def test_multigraph(self):
G = nx.MultiGraph()
nx.add_cycle(G, [0, 1, 2, 3])
G.add_edge(1, 2)
G.add_edge(1, 2)
edges = list(nx.eulerian_circuit(G, source=0))
nodes = [u for u, v in edges]
assert nodes == [0, 3, 2, 1, 2, 1]
assert edges == [(0, 3), (3, 2), (2, 1), (1, 2), (2, 1), (1, 0)]
def test_multigraph_with_keys(self):
G = nx.MultiGraph()
nx.add_cycle(G, [0, 1, 2, 3])
G.add_edge(1, 2)
G.add_edge(1, 2)
edges = list(nx.eulerian_circuit(G, source=0, keys=True))
nodes = [u for u, v, k in edges]
assert nodes == [0, 3, 2, 1, 2, 1]
assert edges[:2] == [(0, 3, 0), (3, 2, 0)]
assert collections.Counter(edges[2:5]) == collections.Counter(
[(2, 1, 0), (1, 2, 1), (2, 1, 2)]
)
assert edges[5:] == [(1, 0, 0)]
def test_not_eulerian(self):
with pytest.raises(nx.NetworkXError):
f = list(nx.eulerian_circuit(nx.complete_graph(4)))
class TestIsSemiEulerian:
def test_is_semieulerian(self):
# Test graphs with Eulerian paths but no cycles return True.
assert nx.is_semieulerian(nx.path_graph(4))
G = nx.path_graph(6, create_using=nx.DiGraph)
assert nx.is_semieulerian(G)
# Test graphs with Eulerian cycles return False.
assert not nx.is_semieulerian(nx.complete_graph(5))
assert not nx.is_semieulerian(nx.complete_graph(7))
assert not nx.is_semieulerian(nx.hypercube_graph(4))
assert not nx.is_semieulerian(nx.hypercube_graph(6))
class TestHasEulerianPath:
def test_has_eulerian_path_cyclic(self):
# Test graphs with Eulerian cycles return True.
assert nx.has_eulerian_path(nx.complete_graph(5))
assert nx.has_eulerian_path(nx.complete_graph(7))
assert nx.has_eulerian_path(nx.hypercube_graph(4))
assert nx.has_eulerian_path(nx.hypercube_graph(6))
def test_has_eulerian_path_non_cyclic(self):
# Test graphs with Eulerian paths but no cycles return True.
assert nx.has_eulerian_path(nx.path_graph(4))
G = nx.path_graph(6, create_using=nx.DiGraph)
assert nx.has_eulerian_path(G)
def test_has_eulerian_path_directed_graph(self):
# Test directed graphs and returns False
G = nx.DiGraph()
G.add_edges_from([(0, 1), (1, 2), (0, 2)])
assert not nx.has_eulerian_path(G)
# Test directed graphs without isolated node returns True
G = nx.DiGraph()
G.add_edges_from([(0, 1), (1, 2), (2, 0)])
assert nx.has_eulerian_path(G)
# Test directed graphs with isolated node returns False
G.add_node(3)
assert not nx.has_eulerian_path(G)
@pytest.mark.parametrize("G", (nx.Graph(), nx.DiGraph()))
def test_has_eulerian_path_not_weakly_connected(self, G):
G.add_edges_from([(0, 1), (2, 3), (3, 2)])
assert not nx.has_eulerian_path(G)
@pytest.mark.parametrize("G", (nx.Graph(), nx.DiGraph()))
def test_has_eulerian_path_unbalancedins_more_than_one(self, G):
G.add_edges_from([(0, 1), (2, 3)])
assert not nx.has_eulerian_path(G)
class TestFindPathStart:
def testfind_path_start(self):
find_path_start = nx.algorithms.euler._find_path_start
# Test digraphs return correct starting node.
G = nx.path_graph(6, create_using=nx.DiGraph)
assert find_path_start(G) == 0
edges = [(0, 1), (1, 2), (2, 0), (4, 0)]
assert find_path_start(nx.DiGraph(edges)) == 4
# Test graph with no Eulerian path return None.
edges = [(0, 1), (1, 2), (2, 3), (2, 4)]
assert find_path_start(nx.DiGraph(edges)) is None
class TestEulerianPath:
def test_eulerian_path(self):
x = [(4, 0), (0, 1), (1, 2), (2, 0)]
for e1, e2 in zip(x, nx.eulerian_path(nx.DiGraph(x))):
assert e1 == e2
def test_eulerian_path_straight_link(self):
G = nx.DiGraph()
result = [(1, 2), (2, 3), (3, 4), (4, 5)]
G.add_edges_from(result)
assert result == list(nx.eulerian_path(G))
assert result == list(nx.eulerian_path(G, source=1))
with pytest.raises(nx.NetworkXError):
list(nx.eulerian_path(G, source=3))
with pytest.raises(nx.NetworkXError):
list(nx.eulerian_path(G, source=4))
with pytest.raises(nx.NetworkXError):
list(nx.eulerian_path(G, source=5))
def test_eulerian_path_multigraph(self):
G = nx.MultiDiGraph()
result = [(2, 1), (1, 2), (2, 1), (1, 2), (2, 3), (3, 4), (4, 3)]
G.add_edges_from(result)
assert result == list(nx.eulerian_path(G))
assert result == list(nx.eulerian_path(G, source=2))
with pytest.raises(nx.NetworkXError):
list(nx.eulerian_path(G, source=3))
with pytest.raises(nx.NetworkXError):
list(nx.eulerian_path(G, source=4))
def test_eulerian_path_eulerian_circuit(self):
G = nx.DiGraph()
result = [(1, 2), (2, 3), (3, 4), (4, 1)]
result2 = [(2, 3), (3, 4), (4, 1), (1, 2)]
result3 = [(3, 4), (4, 1), (1, 2), (2, 3)]
G.add_edges_from(result)
assert result == list(nx.eulerian_path(G))
assert result == list(nx.eulerian_path(G, source=1))
assert result2 == list(nx.eulerian_path(G, source=2))
assert result3 == list(nx.eulerian_path(G, source=3))
def test_eulerian_path_undirected(self):
G = nx.Graph()
result = [(1, 2), (2, 3), (3, 4), (4, 5)]
result2 = [(5, 4), (4, 3), (3, 2), (2, 1)]
G.add_edges_from(result)
assert list(nx.eulerian_path(G)) in (result, result2)
assert result == list(nx.eulerian_path(G, source=1))
assert result2 == list(nx.eulerian_path(G, source=5))
with pytest.raises(nx.NetworkXError):
list(nx.eulerian_path(G, source=3))
with pytest.raises(nx.NetworkXError):
list(nx.eulerian_path(G, source=2))
def test_eulerian_path_multigraph_undirected(self):
G = nx.MultiGraph()
result = [(2, 1), (1, 2), (2, 1), (1, 2), (2, 3), (3, 4)]
G.add_edges_from(result)
assert result == list(nx.eulerian_path(G))
assert result == list(nx.eulerian_path(G, source=2))
with pytest.raises(nx.NetworkXError):
list(nx.eulerian_path(G, source=3))
with pytest.raises(nx.NetworkXError):
list(nx.eulerian_path(G, source=1))
@pytest.mark.parametrize(
("graph_type", "result"),
(
(nx.MultiGraph, [(0, 1, 0), (1, 0, 1)]),
(nx.MultiDiGraph, [(0, 1, 0), (1, 0, 0)]),
),
)
def test_eulerian_with_keys(self, graph_type, result):
G = graph_type([(0, 1), (1, 0)])
answer = nx.eulerian_path(G, keys=True)
assert list(answer) == result
class TestEulerize:
def test_disconnected(self):
with pytest.raises(nx.NetworkXError):
G = nx.from_edgelist([(0, 1), (2, 3)])
nx.eulerize(G)
def test_null_graph(self):
with pytest.raises(nx.NetworkXPointlessConcept):
nx.eulerize(nx.Graph())
def test_null_multigraph(self):
with pytest.raises(nx.NetworkXPointlessConcept):
nx.eulerize(nx.MultiGraph())
def test_on_empty_graph(self):
with pytest.raises(nx.NetworkXError):
nx.eulerize(nx.empty_graph(3))
def test_on_eulerian(self):
G = nx.cycle_graph(3)
H = nx.eulerize(G)
assert nx.is_isomorphic(G, H)
def test_on_eulerian_multigraph(self):
G = nx.MultiGraph(nx.cycle_graph(3))
G.add_edge(0, 1)
H = nx.eulerize(G)
assert nx.is_eulerian(H)
def test_on_complete_graph(self):
G = nx.complete_graph(4)
assert nx.is_eulerian(nx.eulerize(G))
assert nx.is_eulerian(nx.eulerize(nx.MultiGraph(G)))
def test_on_non_eulerian_graph(self):
G = nx.cycle_graph(18)
G.add_edge(0, 18)
G.add_edge(18, 19)
G.add_edge(17, 19)
G.add_edge(4, 20)
G.add_edge(20, 21)
G.add_edge(21, 22)
G.add_edge(22, 23)
G.add_edge(23, 24)
G.add_edge(24, 25)
G.add_edge(25, 26)
G.add_edge(26, 27)
G.add_edge(27, 28)
G.add_edge(28, 13)
assert not nx.is_eulerian(G)
G = nx.eulerize(G)
assert nx.is_eulerian(G)
assert nx.number_of_edges(G) == 39
|
