def test_franklin(self):
""" 12-vertex cubic graph: non-planar but hamiltonian """
expected = False
actual = is_planar(nx.LCF_graph(12, [5, -5], 6))
self.assertEqual(expected, actual)
actual = is_planar(nx.LCF_graph(12, [-5, -3, 3, 5], 3))
self.assertEqual(expected, actual)
def gen():
g = nx.LCF_graph(20, [1, 3, 14], 5)
pairs = [(0, 12), (1, 5), (1, 19), (2, 11), (3, 4),
(3, 9), (3, 18), (6, 15), (10, 14)]
print pairs
costs = [1] * nx.number_of_edges(g) * 2
return (g, costs, pairs)
def test_harries(self):
expected = False
actual = is_planar(
nx.LCF_graph(70, [
-29, -19, -13, 13, 21, -27, 27, 33, -13, 13, 19, -21, -33, 29
], 5))
self.assertEqual(expected, actual)
def gen():
g1 = nx.frucht_graph()
g2 = nx.LCF_graph(12, [-5, -2, -4, 2, 5, -2, 2, 5, -2, -5, 4, 2], 1)
# print(nx.is_isomorphic(g1, g2))
# g1 = nx.cubical_graph()
# g2 = nx.LCF_graph(8, [3, -3], 4)
return g1, g2
def test_tutte_12_cage(self):
expected = False
actual = is_planar(
nx.LCF_graph(126, [
17, 27, -13, -59, -35, 35, -11, 13, -53, 53, -27, 21, 57, 11,
-21, -57, 59, -17
], 7))
self.assertEqual(expected, actual)
def gen(k):
g = nx.LCF_graph(20, [1, 3, 14], 5)
for u, v in g.edges_iter():
g[u][v]['cost'] = 2
random.seed(3)
srcs = random.sample(range(g.number_of_nodes()), k)
return (g, srcs)
def test__LCF_graph(self):
# If n<=0, then return the null_graph
G = nx.LCF_graph(-10, [1, 2], 100)
assert is_isomorphic(G, null)
G = nx.LCF_graph(0, [1, 2], 3)
assert is_isomorphic(G, null)
G = nx.LCF_graph(0, [1, 2], 10)
assert is_isomorphic(G, null)
# Test that LCF(n,[],0) == cycle_graph(n)
for a, b, c in [(5, [], 0), (10, [], 0), (5, [], 1), (10, [], 10)]:
G = nx.LCF_graph(a, b, c)
assert is_isomorphic(G, nx.cycle_graph(a))
# Generate the utility graph K_{3,3}
G = nx.LCF_graph(6, [3, -3], 3)
utility_graph = nx.complete_bipartite_graph(3, 3)
assert is_isomorphic(G, utility_graph)
def test_Ljubljana(self):
expected = False
actual = is_planar(
nx.LCF_graph(26, [
47, -23, -31, 39, 25, -21, -31, -41, 25, 15, 29, -41, -19, 15,
-49, 33, 39, -35, -21, 17, -33, 49, 41, 31, -15, -29, 41, 31,
-15, -25, 21, 31, -51, -25, 23, 9, -17, 51, 35, -29, 21, -51,
-39, 33, -9, -51, 51, -47, -33, 19, 51, -21, 29, 21, -31, -39
], 2))
self.assertEqual(expected, actual)
def test_harries_wong(self):
expected = False
actual = is_planar(
nx.LCF_graph(70, [
9, 25, 31, -17, 17, 33, 9, -29, -15, -9, 9, 25, -25, 29, 17,
-9, 9, -27, 35, -9, 9, -17, 21, 27, -29, -9, -25, 13, 19, -9,
-33, -17, 19, -31, 27, 11, -25, 29, -33, 13, -13, 21, -29, -21,
25, 9, -11, -19, 29, 9, -27, -19, -13, -35, -9, 9, 17, 25, -9,
9, 27, -27, -21, 15, -9, 29, -29, 33, -9, -25
], 1))
self.assertEqual(expected, actual)
def test_balaban_10(self):
expected = False
actual = is_planar(
nx.LCF_graph(70, [
68, -25, -18, 29, 13, 35, -13, -29, 19, 25, 9, -29, 29, 17, 33,
21, 9, -13, -31, -9, 25, 17, 9, -31, 27, -9, 17, -19, -29, 27,
-17, -9, -29, 33, -25, 25, -21, 17, -17, 29, 35, -29, 17, -17,
21, -25, 25, -33, 29, 9, 17, -27, 29, 19, -17, 9, -27, 31, -9,
-17, -25, 9, 31, 13, -9, -21, -33, -17, -29, 29
], 1))
self.assertEqual(expected, actual)
def test_biggs_smith(self):
expected = False
actual = is_planar(
nx.LCF_graph(102, [
16, 24, -38, 17, 34, 48, -19, 41, -35, 47, -20, 34, -36, 21,
14, 48, -16, -36, -43, 28, -17, 21, 29, -43, 46, -24, 28, -38,
-14, -50, -45, 21, 8, 27, -21, 20, -37, 39, -34, -44, -8, 38,
-21, 25, 15, -34, 18, -28, -41, 36, 8, -29, -21, -48, -28, -20,
-47, 14, -8, -15, -27, 38, 24, -48, -18, 25, 38, 31, -25, 24,
-46, -14, 28, 11, 21, 35, -39, 43, 36, -38, 14, 50, 43, 36,
-11, -36, -24, 45, 8, 19, -25, 38, 20, -24, -14, -21, -8, 44,
-31, -38, -28, 37
], 1))
self.assertEqual(expected, actual)
def test_balaban_11(self):
expected = False
actual = is_planar(
nx.LCF_graph(112, [
44, 26, -47, -15, 35, -39, 11, -27, 38, -37, 43, 14, 28, 51,
-29, -16, 41, -11, -26, 15, 22, -51, -35, 36, 52, -14, -33,
-26, -46, 52, 26, 16, 43, 33, -15, 17, -53, 23, -42, -35, -28,
30, -22, 45, -44, 16, -38, -16, 50, -55, 20, 28, -17, -43, 47,
34, -26, -41, 11, -36, -23, -16, 41, 17, -51, 26, -33, 47, 17,
-11, -20, -30, 21, 29, 36, -43, -52, 10, 39, -28, -17, -52, 51,
26, 37, -17, 10, -10, -45, -34, 17, -26, 27, -21, 46, 53, -10,
29, -50, 35, 15, -47, -29, -41, 26, 33, 55, -17, 42, -26, -36,
16
], 1))
self.assertEqual(expected, actual)
def gen():
g1 = nx.frucht_graph()
g2 = nx.LCF_graph(12, [-5, -2, -4, 2, 5, -2, 2, 5, -2, -5, 4, 2], 1)
return g1, g2
def test_tutte_coxeter(self):
expected = False
actual = is_planar(nx.LCF_graph(26, [-13, -9, 7, -7, 9, 13], 5))
self.assertEqual(expected, actual)
def test_f26a(self):
expected = False
actual = is_planar(nx.LCF_graph(26, [-7, 7], 13))
self.assertEqual(expected, actual)
def test_naruru(self):
expected = False
actual = is_planar(nx.LCF_graph(24, [5, -9, 7, -7, 9, -5], 4))
self.assertEqual(expected, actual)
def test_bidiakis_cube(self):
expected = True
actual = is_planar(nx.LCF_graph(12, [6, 4, -4], 4))
self.assertEqual(expected, actual)
def test_mcgee(self):
""" 24-vertex 7-cage graph: non-planar """
expected = False
actual = is_planar(nx.LCF_graph(24, [-12, 7, -7], 8))
self.assertEqual(expected, actual)
def small_graphs():
print("Make small graph")
G = nx.make_small_graph(
["adjacencylist", "C_4", 4, [[2, 4], [1, 3], [2, 4], [1, 3]]])
draw_graph(G)
G = nx.make_small_graph(
["adjacencylist", "C_4", 4, [[2, 4], [3], [4], []]])
draw_graph(G)
G = nx.make_small_graph(
["edgelist", "C_4", 4, [[1, 2], [3, 4], [2, 3], [4, 1]]])
draw_graph(G)
print("LCF graph")
G = nx.LCF_graph(6, [3, -3], 3)
draw_graph(G)
G = nx.LCF_graph(14, [5, -5], 7)
draw_graph(G)
print("Bull graph")
G = nx.bull_graph()
draw_graph(G)
print("Chvátal graph")
G = nx.chvatal_graph()
draw_graph(G)
print("Cubical graph")
G = nx.cubical_graph()
draw_graph(G)
print("Desargues graph")
G = nx.desargues_graph()
draw_graph(G)
print("Diamond graph")
G = nx.diamond_graph()
draw_graph(G)
print("Dodechaedral graph")
G = nx.dodecahedral_graph()
draw_graph(G)
print("Frucht graph")
G = nx.frucht_graph()
draw_graph(G)
print("Heawood graph")
G = nx.heawood_graph()
draw_graph(G)
print("House graph")
G = nx.house_graph()
draw_graph(G)
print("House X graph")
G = nx.house_x_graph()
draw_graph(G)
print("Icosahedral graph")
G = nx.icosahedral_graph()
draw_graph(G)
print("Krackhardt kite graph")
G = nx.krackhardt_kite_graph()
draw_graph(G)
print("Moebius kantor graph")
G = nx.moebius_kantor_graph()
draw_graph(G)
print("Octahedral graph")
G = nx.octahedral_graph()
draw_graph(G)
print("Pappus graph")
G = nx.pappus_graph()
draw_graph(G)
print("Petersen graph")
G = nx.petersen_graph()
draw_graph(G)
print("Sedgewick maze graph")
G = nx.sedgewick_maze_graph()
draw_graph(G)
print("Tetrahedral graph")
G = nx.tetrahedral_graph()
draw_graph(G)
print("Truncated cube graph")
G = nx.truncated_cube_graph()
draw_graph(G)
print("Truncated tetrahedron graph")
G = nx.truncated_tetrahedron_graph()
draw_graph(G)
print("Tutte graph")
G = nx.tutte_graph()
draw_graph(G)
def test_gray(self):
expected = False
actual = is_planar(nx.LCF_graph(54, [-25, 7, -7, 13, -13, 25], 9))
self.assertEqual(expected, actual)
def test_dyck(self):
expected = False
actual = is_planar(nx.LCF_graph(32, [-13, 5, -5, 13], 8))
self.assertEqual(expected, actual)
def test_levi(self):
""" 30-vertex incidence graph: non-planar """
expected = False
actual = is_planar(nx.LCF_graph(30, [-13, -9, 7, -7, 9, 13], 5))
self.assertEqual(expected, actual)
def gen():
G = nx.LCF_graph(20, [1, 3, 14], 5)
for i, j in G.edges():
G[i][j]['weight'] = 2
return G
def test_utility(self):
expected = False
actual = is_planar(nx.LCF_graph(6, [3, -3], 3))
self.assertEqual(expected, actual)
import picos as pic
import networkx as nx
#number of nodes
N = 20
#Generate a graph with LCF notation (you can change the values below to obtain another graph!)
#We use this deterministic generator in order to have a constant inuput for doctest.
G = nx.LCF_graph(N, [1, 3, 14], 5)
G = nx.DiGraph(G) #edges are bidirected
#generate edge capacities
c = {}
for i, e in enumerate(G.edges()):
c[e] = ((-2)**i) % 17 #an arbitrary sequence of numbers
#-------------#
# min cut #
#-------------#
mincut = pic.Problem()
#source and sink nodes
s = 16
t = 10
#convert the capacities as a picos expression
cc = pic.new_param('c', c)
#cut variable
d = {}
def test_foster(self):
expected = False
actual = is_planar(nx.LCF_graph(90, [17, -9, 37, -37, 9, -17], 15))
self.assertEqual(expected, actual)
