else:
G_cap[i][j] = delta
print('Network capacity')
print(G_cap)
print('\n')
# Set setUniverse
universe = []
for i in range(0, N):
for j in range(0, N):
if (i < j and G_connect[i][j] == 1):
universe.append((i, j))
GraphSet.set_universe(universe)
gc = GraphSet.connected_components(range(N)) #Graphset with connectivity
#print(gc.len())
nk = Count_nk(gc) #the number of non-connected failure pattern
print('The number of non-connected failure pattern')
print(nk)
print('\n')
num_fp = []
for i in range(0, E + 1):
num_fp.append(int(comb(E, i) -
nk[i])) #the number of connected failure pattern
print('The number of connected failure pattern')
print(num_fp)
print('\n')
def test_graphs(self):
GraphSet.set_universe([(1, 2), (1, 4), (2, 3), (2, 5), (3, 6), (4, 5),
(5, 6)])
# any subgraph
gs = GraphSet.graphs()
self.assertTrue(isinstance(gs, GraphSet))
self.assertEqual(len(gs), 2**7)
self.assertTrue([(1, 2)] in gs)
# subgraphs separating [1, 5] and [2]
gs = GraphSet.graphs(vertex_groups=[[1, 5], [2]])
self.assertEqual(len(gs), 6)
self.assertTrue([(1, 4), (4, 5)] in gs)
self.assertTrue([(1, 2), (1, 4), (4, 5)] not in gs)
# matching
dc = {}
for v in range(1, 7):
dc[v] = range(0, 2)
gs = GraphSet.graphs(degree_constraints=dc)
self.assertEqual(len(gs), 22)
self.assertTrue([(1, 2), (3, 6)] in gs)
self.assertTrue([(1, 2), (2, 3), (3, 6)] not in gs)
for g in gs:
self.assertTrue(len(g) < 4)
# subgraphs with 1 or 2 edges
gs = GraphSet.graphs(num_edges=range(1, 3))
self.assertEqual(len(gs), 28)
for g in gs:
self.assertTrue(1 <= len(g) and len(g) < 3)
# single connected component and vertex islands
gs = GraphSet.graphs(vertex_groups=[[]])
self.assertEqual(len(gs), 80)
self.assertTrue([(1, 2), (2, 3)] in gs)
self.assertTrue([(1, 2), (2, 3), (4, 5)] not in gs)
# any forest
gs = GraphSet.graphs(no_loop=True)
self.assertEqual(len(gs), 112)
self.assertTrue([(1, 2), (1, 4), (2, 5)] in gs)
self.assertTrue([(1, 2), (1, 4), (2, 5), (4, 5)] not in gs)
for g in gs:
self.assertTrue(len(g) < 6)
# constrained by GraphSet
gs = GraphSet.graphs(no_loop=True)
gs = gs.graphs(vertex_groups=[[]])
self.assertEqual(len(gs), 66)
self.assertTrue([(1, 2), (1, 4), (2, 5)] in gs)
self.assertTrue([(1, 2), (1, 4), (2, 5), (4, 5)] not in gs)
# single connected components across 1, 3, and 5
gs = GraphSet.connected_components([1, 3, 5])
self.assertEqual(len(gs), 35)
self.assertTrue([(1, 2), (2, 3), (2, 5)] in gs)
self.assertTrue([(1, 2), (2, 3), (5, 6)] not in gs)
GraphSet.set_universe([(1, 2), (1, 3), (1, 4), (1, 5), (2, 3), (2, 4),
(2, 5), (3, 4), (3, 5), (4, 5)])
# cliques with 4 vertices
gs = GraphSet.cliques(4)
self.assertEqual(len(gs), 5)
self.assertTrue([(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)] in gs)
self.assertTrue([(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 5)] not in gs)
GraphSet.set_universe([(1, 2), (1, 4), (2, 3), (2, 5), (3, 6), (4, 5),
(5, 6)])
# trees rooted at 1
gs = GraphSet.trees(1)
self.assertEqual(len(gs), 45)
self.assertTrue([] in gs)
self.assertTrue([(1, 2), (1, 4), (2, 5), (4, 5)] not in gs)
# spanning trees
gs = GraphSet.trees(is_spanning=True)
self.assertEqual(len(gs), 15)
self.assertTrue([(1, 2), (1, 4), (2, 3), (2, 5), (3, 6)] in gs)
self.assertTrue([(1, 2), (1, 4), (2, 3), (2, 5), (4, 5)] not in gs)
for g in gs:
self.assertEqual(len(g), 5)
# forests rooted at 1 and 3
gs = GraphSet.forests([1, 3])
self.assertEqual(len(gs), 54)
self.assertTrue([] in gs)
self.assertTrue([(1, 2), (2, 3)] not in gs)
# spanning forests rooted at 1 and 3
gs = GraphSet.forests([1, 3], is_spanning=True)
self.assertEqual(len(gs), 20)
self.assertTrue([(1, 2), (1, 4), (2, 5), (3, 6)] in gs)
self.assertTrue([(1, 2), (1, 4), (2, 3), (2, 5)] not in gs)
for g in gs:
self.assertEqual(len(g), 4)
# cycles
gs = GraphSet.cycles()
self.assertEqual(len(gs), 3)
self.assertTrue([(1, 2), (1, 4), (2, 5), (4, 5)] in gs)
self.assertTrue([] not in gs)
# hamilton cycles
gs = GraphSet.cycles(is_hamilton=True)
self.assertEqual(len(gs), 1)
self.assertTrue([(1, 2), (1, 4), (2, 3), (3, 6), (4, 5), (5, 6)] in gs)
# paths between 1 and 6
gs = GraphSet.paths(1, 6)
self.assertEqual(len(gs), 4)
self.assertTrue([(1, 2), (2, 3), (3, 6)] in gs)
self.assertTrue([(1, 2), (2, 3), (5, 6)] not in gs)
# hamilton paths between 1 and 6
gs = GraphSet.paths(1, 6, is_hamilton=True)
self.assertEqual(len(gs), 1)
self.assertTrue([(1, 4), (2, 3), (2, 5), (3, 6), (4, 5)] in gs)
# called as instance methods
gs = GraphSet.graphs(no_loop=True)
_ = gs.connected_components([1, 3, 5])
_ = gs.cliques(4)
_ = gs.trees(1)
_ = gs.forests([1, 3])
_ = gs.cycles()
_ = gs.paths(1, 6)
# exceptions
self.assertRaises(KeyError, GraphSet.graphs, vertex_groups=[[7]])
self.assertRaises(KeyError, GraphSet.graphs, degree_constraints={7: 1})
def test_graphs(self):
GraphSet.set_universe([(1, 2), (1, 4), (2, 3), (2, 5), (3, 6), (4, 5),
(5, 6)])
# any subgraph
gs = GraphSet.graphs()
self.assertTrue(isinstance(gs, GraphSet))
self.assertEqual(len(gs), 2**7)
self.assertTrue([(1, 2)] in gs)
# subgraphs separating [1, 5] and [2]
gs = GraphSet.graphs(vertex_groups=[[1, 5], [2]])
self.assertEqual(len(gs), 6)
self.assertTrue([(1, 4), (4, 5)] in gs)
self.assertTrue([(1, 2), (1, 4), (4, 5)] not in gs)
# matching
dc = {}
for v in range(1, 7):
dc[v] = range(0, 2)
gs = GraphSet.graphs(degree_constraints=dc)
self.assertEqual(len(gs), 22)
self.assertTrue([(1, 2), (3, 6)] in gs)
self.assertTrue([(1, 2), (2, 3), (3, 6)] not in gs)
for g in gs:
self.assertTrue(len(g) < 4)
# subgraphs with 1 or 2 edges
gs = GraphSet.graphs(num_edges=range(1, 3))
self.assertEqual(len(gs), 28)
for g in gs:
self.assertTrue(1 <= len(g) and len(g) < 3)
# single connected component and vertex islands
gs = GraphSet.graphs(vertex_groups=[[]])
self.assertEqual(len(gs), 80)
self.assertTrue([(1, 2), (2, 3)] in gs)
self.assertTrue([(1, 2), (2, 3), (4, 5)] not in gs)
# any forest
gs = GraphSet.graphs(no_loop=True)
self.assertEqual(len(gs), 112)
self.assertTrue([(1, 2), (1, 4), (2, 5)] in gs)
self.assertTrue([(1, 2), (1, 4), (2, 5), (4, 5)] not in gs)
for g in gs:
self.assertTrue(len(g) < 6)
# constrained by GraphSet
gs = GraphSet.graphs(no_loop=True)
gs = gs.graphs(vertex_groups=[[]])
self.assertEqual(len(gs), 66)
self.assertTrue([(1, 2), (1, 4), (2, 5)] in gs)
self.assertTrue([(1, 2), (1, 4), (2, 5), (4, 5)] not in gs)
# single connected components across 1, 3, and 5
gs = GraphSet.connected_components([1, 3, 5])
self.assertEqual(len(gs), 35)
self.assertTrue([(1, 2), (2, 3), (2, 5)] in gs)
self.assertTrue([(1, 2), (2, 3), (5, 6)] not in gs)
GraphSet.set_universe([(1, 2), (1, 3), (1, 4), (1, 5), (2, 3), (2, 4),
(2, 5), (3, 4), (3, 5), (4, 5)])
# cliques with 4 vertices
gs = GraphSet.cliques(4)
self.assertEqual(len(gs), 5)
self.assertTrue([(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)] in gs)
self.assertTrue([(1, 2), (1, 3), (1, 4), (2, 3), (2,
4), (3,
5)] not in gs)
GraphSet.set_universe([(1, 2), (1, 4), (2, 3), (2, 5), (3, 6), (4, 5),
(5, 6)])
# trees rooted at 1
gs = GraphSet.trees(1)
self.assertEqual(len(gs), 45)
self.assertTrue([] in gs)
self.assertTrue([(1, 2), (1, 4), (2, 5), (4, 5)] not in gs)
# spanning trees
gs = GraphSet.trees(is_spanning=True)
self.assertEqual(len(gs), 15)
self.assertTrue([(1, 2), (1, 4), (2, 3), (2, 5), (3, 6)] in gs)
self.assertTrue([(1, 2), (1, 4), (2, 3), (2, 5), (4, 5)] not in gs)
for g in gs:
self.assertEqual(len(g), 5)
# forests rooted at 1 and 3
gs = GraphSet.forests([1, 3])
self.assertEqual(len(gs), 54)
self.assertTrue([] in gs)
self.assertTrue([(1, 2), (2, 3)] not in gs)
# spanning forests rooted at 1 and 3
gs = GraphSet.forests([1, 3], is_spanning=True)
self.assertEqual(len(gs), 20)
self.assertTrue([(1, 2), (1, 4), (2, 5), (3, 6)] in gs)
self.assertTrue([(1, 2), (1, 4), (2, 3), (2, 5)] not in gs)
for g in gs:
self.assertEqual(len(g), 4)
# cycles
gs = GraphSet.cycles()
self.assertEqual(len(gs), 3)
self.assertTrue([(1, 2), (1, 4), (2, 5), (4, 5)] in gs)
self.assertTrue([] not in gs)
# hamilton cycles
gs = GraphSet.cycles(is_hamilton=True)
self.assertEqual(len(gs), 1)
self.assertTrue([(1, 2), (1, 4), (2, 3), (3, 6), (4, 5), (5, 6)] in gs)
# paths between 1 and 6
gs = GraphSet.paths(1, 6)
self.assertEqual(len(gs), 4)
self.assertTrue([(1, 2), (2, 3), (3, 6)] in gs)
self.assertTrue([(1, 2), (2, 3), (5, 6)] not in gs)
# hamilton paths between 1 and 6
gs = GraphSet.paths(1, 6, is_hamilton=True)
self.assertEqual(len(gs), 1)
self.assertTrue([(1, 4), (2, 3), (2, 5), (3, 6), (4, 5)] in gs)
# called as instance methods
gs = GraphSet.graphs(no_loop=True)
_ = gs.connected_components([1, 3, 5])
_ = gs.cliques(4)
_ = gs.trees(1)
_ = gs.forests([1, 3])
_ = gs.cycles()
_ = gs.paths(1, 6)
# exceptions
self.assertRaises(KeyError, GraphSet.graphs, vertex_groups=[[7]])
self.assertRaises(KeyError, GraphSet.graphs, degree_constraints={7: 1})
