def cube_algorithm(G_complete):
"""
Use cube algorithm to build an approximation for the 2-MBST problem on G:
1. Add edges to G to build complete graph G_complete
2. Build an MST T of G_complete
3. Build the the cube of T
4. find a Hamiltonian path in the cube of T
:param G : (nx.Graph())
"""
T = nx.minimum_spanning_tree(G_complete, weight="weight")
T_cube = nx.Graph()
T_cube.add_nodes_from(T.nodes(data=True))
shortest_paths = nx.shortest_path_length(T)
for source, lengths_dict in shortest_paths:
for target in lengths_dict:
if lengths_dict[target] <= 3:
T_cube.add_edge(source,
target,
weight=G_complete.get_edge_data(
source, target)["weight"])
ham_path = hamiltonian_path(T_cube.to_directed())
result = nx.Graph()
result.add_nodes_from(G_complete.nodes(data=True))
for idx in range(len(ham_path) - 1):
result.add_edge(ham_path[idx],
ham_path[idx + 1],
weight=G_complete.get_edge_data(
ham_path[idx], ham_path[idx + 1])['weight'])
return result
def test_hamiltonian_cycle(self):
"""TestData that :func:`networkx.tournament.hamiltonian_path`
returns a Hamiltonian cycle when provided a strongly connected
tournament.
"""
G = DiGraph()
G.add_edges_from([(0, 1), (1, 2), (2, 3), (3, 0), (1, 3), (0, 2)])
path = hamiltonian_path(G)
assert len(path) == 4
assert all(v in G[u] for u, v in zip(path, path[1:]))
assert path[0] in G[path[-1]]
def test_hamiltonian_cycle(self):
"""Tests that :func:`networkx.tournament.hamiltonian_path`
returns a Hamiltonian cycle when provided a strongly connected
tournament.
"""
G = DiGraph()
G.add_edges_from([(0, 1), (1, 2), (2, 3), (3, 0), (1, 3), (0, 2)])
path = hamiltonian_path(G)
assert_equal(len(path), 4)
assert_true(all(v in G[u] for u, v in zip(path, path[1:])))
assert_true(path[0] in G[path[-1]])
def test_path_is_hamiltonian(self):
G = DiGraph()
G.add_edges_from([(0, 1), (1, 2), (2, 3), (3, 0), (1, 3), (0, 2)])
path = hamiltonian_path(G)
assert len(path) == 4
assert all(v in G[u] for u, v in zip(path, path[1:]))
def test_path_is_hamiltonian(self):
G = DiGraph()
G.add_edges_from([(0, 1), (1, 2), (2, 3), (3, 0), (1, 3), (0, 2)])
path = hamiltonian_path(G)
assert_equal(len(path), 4)
assert_true(all(v in G[u] for u, v in zip(path, path[1:])))
# g) Maximum matching
print("g) M =", nx.max_weight_matching(G))
print()
# h) Minimum vertex cover
print("h) R =", vertex_cover.min_weighted_vertex_cover(G))
print()
# i) Minimum edge cover
print("i) F =", covering.min_edge_cover(G))
print()
# j) Shortest closed path (circuit) that visits every vertex
print("j) W =", end=" ")
for i in range(len(tournament.hamiltonian_path(D))):
print(tournament.hamiltonian_path(D)[i], "-", end=" ")
print(tournament.hamiltonian_path(D)[0])
print()
# k) Shortest closed path (circuit) that visits every edge
H = nx.eulerize(G)
c = list(n for (n, d) in nx.eulerian_circuit(H))
print("k) U =", end=" ")
for i in range(len(c)):
print(c[i], "-", end=" ")
print(c[0])
print()
# m) 2-edge-connected components
print("m) ", list(edge_kcomponents.bridge_components(G)))
#g
print("Maximum matching")
print(nx.max_weight_matching(g2, maxcardinality=True, weight=0))
#i
print("Minimum edge cover")
print(covering.min_edge_cover(g2)) #ищем минимальное реберное покрытие
#j
print("Hanging vertices")
print([u for v, u in g3.edges() if len(g3[u]) == 1]) #узнаем висячие вершины
g3.remove_nodes_from([u for v, u in g3.edges()
if len(g3[u]) == 1]) #убираем висячие ребра
print("The shortest closed path that visits every vertex")
print(tournament.hamiltonian_path(
g3)) #ищем гамильтонов путь и добавляем в него высячие ребра
#k
print("The shortest closed path that visits every edge")
print(list(euler.eulerian_circuit(
g3))) #ищем эйлеров путь и добавляем в него ребра-мосты к висячим вершинам
#m
print("2-edge-connected components")
print(list(edge_kcomponents.bridge_components(g)))
#o
mstree = nx.Graph(mst.minimum_spanning_tree(g2))
print("MST")
print(mstree.edges)
print("Weight of MST")
def test_hamiltonian_empty_graph():
path = hamiltonian_path(DiGraph())
assert len(path) == 0