def test_num_variables(self):
G = nx.Graph()
G.add_nodes_from(range(15))
Q = dnx.vertex_color_qubo(G, 7)
bqm = dimod.BinaryQuadraticModel.from_qubo(Q)
self.assertEqual(len(bqm.quadratic), len(G) * 7 * (7 - 1) / 2)
# add one edge
G.add_edge(0, 1)
Q = dnx.vertex_color_qubo(G, 7)
bqm = dimod.BinaryQuadraticModel.from_qubo(Q)
self.assertEqual(len(bqm.quadratic), len(G) * 7 * (7 - 1) / 2 + 7)
def test_chromatic_number(self):
G = nx.cycle_graph('abcd')
# when the chromatic number is fixed this is exactly vertex_color
self.assertEqual(
dnx.min_vertex_color_qubo(G, chromatic_lb=2, chromatic_ub=2),
dnx.vertex_color_qubo(G, 2))
def test_4cycle(self):
G = nx.cycle_graph('abcd')
Q = dnx.vertex_color_qubo(G, 2)
sampleset = dimod.ExactSolver().sample_qubo(Q)
# check that the ground state is a valid coloring
ground_energy = sampleset.first.energy
colorings = []
for sample, en in sampleset.data(['sample', 'energy']):
if en > ground_energy:
break
coloring = {}
for (v, c), val in sample.items():
if val:
coloring[v] = c
self.assertTrue(dnx.is_vertex_coloring(G, coloring))
colorings.append(coloring)
# there are two valid colorings
self.assertEqual(len(colorings), 2)
self.assertEqual(ground_energy, -len(G))
def test_single_node(self):
G = nx.Graph()
G.add_node('a')
# a single color
Q = dnx.vertex_color_qubo(G, ['red'])
self.assertEqual(Q, {(('a', 'red'), ('a', 'red')): -1})
def test_docstring_stats(self):
# get a complex-ish graph
G = nx.karate_club_graph()
colors = range(10)
Q = dnx.vertex_color_qubo(G, colors)
bqm = dimod.BinaryQuadraticModel.from_qubo(Q)
self.assertEqual(len(bqm), len(G) * len(colors))
self.assertEqual(
len(bqm.quadratic),
len(G) * len(colors) * (len(colors) - 1) / 2 +
len(G.edges) * len(colors))
